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## Differential Equations (differential + equation)
Kinds of Differential Equations Terms modified by Differential Equations
## Selected Abstracts## Methods to Derive the Differential Equation of the Free Surface Boundary GROUND WATER, Issue 3 2010Chongxi ChenFirst page of article [source] ## A Cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Phong B. H. LeAbstract In this paper, high-order systems are reformulated as first-order systems, which are then numerically solved by a collocation method. The collocation method is based on Cartesian discretization with 1D-integrated radial basis function networks (1D-IRBFN) (Numer. Meth. Partial Differential Equations 2007; 23:1192,1210). The present method is enhanced by a new boundary interpolation technique based on 1D-IRBFN, which is introduced to obtain variable approximation at irregular points in irregular domains. The proposed method is well suited to problems with mixed boundary conditions on both regular and irregular domains. The main results obtained are (a) the boundary conditions for the reformulated problem are of Dirichlet type only; (b) the integrated RBFN approximation avoids the well-known reduction of convergence rate associated with differential formulations; (c) the primary variable (e.g. displacement, temperature) and the dual variable (e.g. stress, temperature gradient) have similar convergence order; (d) the volumetric locking effects associated with incompressible materials in solid mechanics are alleviated. Numerical experiments show that the proposed method achieves very good accuracy and high convergence rates. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Point-wise decay estimate for the global classical solutions to quasilinear hyperbolic systems MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2009Yi ZhouAbstract In this paper, we first consider the Cauchy problem for quasilinear strictly hyperbolic systems with weak linear degeneracy. The existence of global classical solutions for small and decay initial data was established in (Commun. Partial Differential Equations 1994; 19:1263,1317; Nonlinear Anal. 1997; 28:1299,1322; Chin. Ann. Math. 2004; 25B:37,56). We give a new, very simple proof of this result and also give a sharp point-wise decay estimate of the solution. Then, we consider the mixed initial-boundary-value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in the first quadrant. Under the assumption that the positive eigenvalues are weakly linearly degenerate, the global existence of classical solution with small and decay initial and boundary data was established in (Discrete Continuous Dynamical Systems 2005; 12(1):59,78; Zhou and Yang, in press). We also give a simple proof of this result as well as a sharp point-wise decay estimate of the solution. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## On the invariant measure for the quasi-linear Lasota equation MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2007Antoni Leon DawidowiczAbstract The problem of the existence of the invariant measure is important considering its connections with chaotic behaviour. In the papers (Zesz. Nauk. Uniw. Jagiello,skiego, Pr. Mat. 1982; 23:117,123; Ann. Pol. Math. 1983; XLI:129,137; J. Differential Equations 2004; 196:448,465) the existence of invariant and ergodic measures according to the dynamical system generated by the Lasota equation was proved, i.e. the equation describing the dynamics and becoming different of the population of cells. In this paper, the existence of such measure for the quasi-linear Lasota equation is proved. This measure is the carriage of the measure described by Dawidowicz (Zesz. Nauk. Uniw. Jagiello,skiego, Pr. Mat. 1982; 23:117,123). Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Local energy decay for linear wave equations with non-compactly supported initial data MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2004Ryo IkehataAbstract A local energy decay problem is studied to a typical linear wave equation in an exterior domain. For this purpose, we do not assume any compactness of the support on the initial data. This generalizes a previous famous result due to Morawetz (Comm. Pure Appl. Math. 1961; 14:561,568). In order to prove local energy decay we mainly apply two types of new ideas due to Ikehata,Matsuyama (Sci. Math. Japon. 2002; 55:33,42) and Todorova,Yordanov (J. Differential Equations 2001; 174:464). Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Interaction of elementary waves for scalar conservation laws on a bounded domain MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2003Hongxia LiuAbstract This paper is concerned with the interaction of elementary waves on a bounded domain for scalar conservation laws. The structure and large time asymptotic behaviours of weak entropy solution in the sense of Bardos et al. (Comm. Partial Differential Equations 1979; 4: 1017) are clarified to the initial,boundary problem for scalar conservation laws ut+,(u)x=0 on (0,1) × (0,,), with the initial data u(x,0)=u0(x):=um and the boundary data u(0,t)=u -,u(1,t)=u+, where u±,um are constants, which are not equivalent, and ,,C2 satisfies ,,,>0, ,(0)=f,(0)=0. We also give some global estimates on derivatives of the weak entropy solution. These estimates play important roles in studying the rate of convergence for various approximation methods to scalar conservation laws. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## On a semilinear elliptic equation with singular term and Hardy,Sobolev critical growth MATHEMATISCHE NACHRICHTEN, Issue 8 2007Jianqing ChenArticle first published online: 8 MAY 200Abstract In a previous work [6], we got an exact local behavior to the positive solutions of an elliptic equation. With the help of this exact local behavior, we obtain in this paper the existence of solutions of an equation with Hardy,Sobolev critical growth and singular term by using variational methods. The result obtained here, even in a particular case, relates with a partial (positive) answer to an open problem proposed in: A. Ferrero and F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations, J. Differential Equations 177, 494,522 (2001). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ## Energy properties preserving schemes for Burgers' equation, NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008R. AnguelovAbstract The Burgers' equation, a simplification of the Navier,Stokes equations, is one of the fundamental model equations in gas dynamics, hydrodynamics, and acoustics that illustrates the coupling between convection/advection and diffusion. The kinetic energy enjoys boundedness and monotone decreasing properties that are useful in the study of the asymptotic behavior of the solution. We construct a family of non-standard finite difference schemes, which replicate the energy equality and the properties of the kinetic energy. Our approach is based on Mickens' rule [Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.] of nonlocal approximation of nonlinear terms. More precisely, we propose a systematic nonlocal way of generating approximations that ensure that the trilinear form is identically zero for repeated arguments. We provide numerical experiments that support the theory and demonstrate the power of the non-standard schemes over the classical ones. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source] ## Second-order Galerkin-Lagrange method for the Navier-Stokes equations (retracted article), NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2005Mohamed BensaadaAbstract It has come to the attention of the editors and publisher that an article published in Numerical Methods and Partial Differential Equations, "Second-order Galerkin-Lagrange method for the Navier-Stokes equations," by Mohamed Bensaada, Driss Esselaoui, and Pierre Saramito, Numer Methods Partial Differential Eq 21(6) (2005), 1099,1121 included large portions that were copied from the following paper without proper citation: "Convergence and nonlinear stability of the Lagrange-Galerkin method for the Navier-Stokes equations," Endre Suli, Numerische Mathematik, Vol. 53, No. 4, pp. 459,486 (July, 1988). We have retracted the paper and apologize to Dr. Suli Numer Methods Partial Differential Eq (2007)23(1)211. [source] ## Mechanics with variable-order differential operators ANNALEN DER PHYSIK, Issue 11-12 2003C.F.M. CoimbraAbstract This work presents the novel concept of Variable-Order (VO) Calculus through the description of a simple problem in Mechanics. A mathematical definition for the VO-differential operator that is suitable to mechanical modelling is proposed, and an example concerning the effect of nonuniform viscoelastic frictional forces is described. A numerical method for the solution of Variable Order Differential Equations (VODEs) is proposed. The physical model under study requires mathematical tools that lie beyond the traditional methods of Constant-Order (CO) differential equations. The VO-Calculus formulation is compared to a CO-Calculus model in order to show the limitations of the latter in resolving the transition between the relevant dynamic regimes. [source] ## Hamiltonian particle-mesh simulations for a non-hydrostatic vertical slice model ATMOSPHERIC SCIENCE LETTERS, Issue 4 2009Seoleun ShinAbstract A Lagrangian particle method is developed for the simulation of atmospheric flows in a non-hydrostatic vertical slice model. The proposed particle method is an extension of the Hamiltonian particle mesh (HPM) [Frank J, Gottwald G, Reich S. 2002. The Hamiltonian particle-mesh method. In Meshfree Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering, Vol. 26, Griebel M, Schweitzer M (eds). Springer-Verlag: Berlin Heidelberg; 131,142] and provides preservation of mass, momentum, and energy. We tested the method for the gravity wave test in Skamarock W, Klemp J. 1994. Efficiency and accuracy of the Klemp-Wilhelmson time-splitting technique. Monthly Weather Review 122: 2623,2630 and the bubble experiments in Robert A. 1993. Bubble convection experiments with a semi-implicit formulation of the Euler equations. Journal of the Atmospheric Sciences 50: 1865,1873. The accuracy of the solutions from the HPM simulation is comparable to those reported in these references. A particularly appealing aspect of the method is in its non-diffusive transport of potential temperature. The solutions are maintained smooth largely due to a ,regularization' of pressure, which is controlled carefully to preserve the total energy and the time-reversibility of the model. In case of the bubble experiments, one also needs to regularize the buoyancy contributions. The simulations demonstrate that particle methods are potentially applicable to non-hydrostatic atmospheric flow regimes and that they lead to a highly accurate transport of materially conserved quantities such as potential temperature under adiabatic flow regimes. Copyright © 2009 Royal Meteorological Society [source] ## Simulation and Inference for Stochastic Differential Equations with R Examples by IACUS, S. M. BIOMETRICS, Issue 1 2009Dave CampbellArticle first published online: 17 MAR 200No abstract is available for this article. [source] ## Modelling the progress of light leaf spot (Pyrenopeziza brassicae) on winter oilseed rape (Brassica napus) in relation to leaf wetness and temperature PLANT PATHOLOGY, Issue 2 2001K. PapastamatiA compartmental model was developed to describe the progress with time of light leaf spot (Pyrenopeziza brassicae) on leaves of winter oilseed rape (Brassica napus) during the autumn in the UK. Differential equations described the transition between the four compartments: healthy susceptible leaves, infected symptomless leaves, sporulating symptomless leaves and leaves with necrotic light leaf spot lesions, respectively. The model was fitted to data on the progress of light leaf spot on winter oilseed rape at a single site during the autumn of the 1990,1991 season. Model parameters were used to describe rates of leaf appearance, leaf death, infection by airborne ascospores (primary inoculum) and infection by splash-dispersed conidiospores (secondary inoculum). Infection was dependent on sufficient leaf wetness duration. The model also included delay terms for the latent period between infection and sporulation and the incubation period between infection and the appearance of necrotic light leaf spot lesions. This modified SEIR model formulation gave a reasonable fit to the experimental data. Sensitivity analysis showed that varying the parameter accounting for the rate of infection by ascospores affected the magnitude of the curves after the start of the epidemic, whilst including a parameter for conidiospore infection improved the fit to the data. Use of ascospore counts from different sites and different years showed variation in spore release patterns sufficient to affect model predictions. [source] ## On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations* JOURNAL OF TIME SERIES ANALYSIS, Issue 1 2003A. S. HurnC51; C52; G12 Abstract. A method for estimating the parameters of stochastic differential equations (SDEs) by simulated maximum likelihood is presented. This method is feasible whenever the underlying SDE is a Markov process. Estimates are compared to those generated by indirect inference, discrete and exact maximum likelihood. The technique is illustrated with reference to a one-factor model of the term structure of interest rates using 3-month US Treasury Bill data. [source] ## Solution of the linear diffusion equation for modelling erosion processes with a time varying diffusion coefficient EARTH SURFACE PROCESSES AND LANDFORMS, Issue 10 2008Georgios Aim.Abstract In the present paper the differential equation of the temporal development of a landform (mountain) with a time dependent diffusion coefficient is solved. It is shown that the shape and dimensions of the landform at time t are independent of the specific variation of the diffusion coefficient with time; they only depend on the mean value of the diffusion coefficient in the time interval where the erosion process takes place. Studying the behaviour of the solution of the differential equation in the wave number domain, it is concluded that Fourier analysis may help in estimating, in quantitative terms, the initial dimensions, the age or, alternatively, the value of the diffusion coefficient of the landform. The theoretical predictions are tested on a hill of the southern part of the Ural mountainous region, in order to show how the results of the mathematical analysis can be used in describing, in quantitative terms, the morphological development of landforms due to erosion processes. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## New approaches for non-classically damped system eigenanalysis EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 9 2005Karen KhanlariAbstract This paper presents three new approaches for solving eigenvalue problems of non-classically damped linear dynamics systems with fewer calculations than the conventional state vector approach. In the latter, the second-order differential equation of motion is converted into a first-order system by doubling the size of the matrices. The new approaches simplify the approach and reduce the number of calculations. The mathematical formulations for the proposed approaches are presented and the numerical results compared with the existing method by solving a sample problem with different damping properties. Of the three proposed approaches, the expansion approach was found to be the simplest and fastest to compute. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Critical damping of structures with elastically supported visco-elastic dampers EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2002Yujin LeeAbstract This paper presents a new formulation for critical damping of structures with elastically supported visco-elastic dampers.Owing to the great dependence of damper performance on the support stiffness, this model is inevitable for reliable modelling of structures with visco-elastic dampers. It is shown that the governing equation of free vibration of this model is reduced to a third-order differential equation and the conventional method for defining the critical damping for second-order differential equations cannot be applied to the present model. It is demonstrated that the region of overdamped vibration is finite in contrast to that (semi-infinite) for second-order differential equations and multiple critical damping coefficients exist. However, it turns out that the smaller one is practically meaningful. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Demographic analysis of continuous-time life-history models ECOLOGY LETTERS, Issue 1 2008André M. De RoosAbstract I present a computational approach to calculate the population growth rate, its sensitivity to life-history parameters and associated statistics like the stable population distribution and the reproductive value for exponentially growing populations, in which individual life history is described as a continuous development through time. The method is generally applicable to analyse population growth and performance for a wide range of individual life-history models, including cases in which the population consists of different types of individuals or in which the environment is fluctuating periodically. It complements comparable methods developed for discrete-time dynamics modelled with matrix or integral projection models. The basic idea behind the method is to use Lotka's integral equation for the population growth rate and compute the integral occurring in that equation by integrating an ordinary differential equation, analogous to recently derived methods to compute steady-states of physiologically structured population models. I illustrate application of the method using a number of published life-history models. [source] ## Spatial,temporal marked point processes: a spectrum of stochastic models ENVIRONMETRICS, Issue 3-4 2010Eric RenshawAbstract Many processes that develop through space and time do so in response not only to their own individual growth mechanisms but also in response to interactive pressures induced by their neighbours. The growth of trees in a forest which compete for light and nutrient resources, for example, provides a classic illustration of this general spatial,temporal growth-interaction process. Not only has its mathematical representation proved to be a powerful tool in the study and analysis of marked point patterns since it may easily be simulated, but it has also been shown to be highly flexible in terms of its application since it is robust with respect to incorrect choice of model selection. Moreover, it is highly amenable to maximum likelihood and least squares parameter estimation techniques. Currently the algorithm comprises deterministic growth and interaction coupled with a stochastic arrival and departure mechanism. So for systems with a fixed number of particles there is an inherent lack of randomness. A variety of different stochastic approaches are therefore presented, from the exact event,time model through to the associated stochastic differential equation, taking in time-increment and Tau- and Langevin-Leaping approximations en route. The main algorithm is illustrated through application to forest management and high-intensity packing of hard particle systems, and comparisons are made with the established force biased approach. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A diffusion model with cubic drift: statistical and computational aspects and application to modelling of the global CO2 emission in Spain ENVIRONMETRICS, Issue 1 2007R. GutiérrezAbstract The aim of this work is the study of a new stochastic diffusion model with a cubic-type drift coefficient. The model is considered as the solution of an Ito stochastic differential equation. Using the Ito's stochastic calculus and properties of the Kummer function, the trend functions and steady-state distribution for the process are obtained. Statistical estimation and corresponding computational methodology are established. Finally, the model is applied to modelling and prediction of the global CO2 emission in Spain. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## The Influence of Mass Transfer on a Porous Fuel Cell Electrode FUEL CELLS, Issue 1-2 2004Y.-P. SunAbstract A one-dimensional model for a porous fuel cell electrode using a liquid electrolyte with dissolved reactant is presented. The model consists of a Poisson, second-order ordinary differential equation, describing the effect of the electric field and a one-dimensional; Fickian diffusion, second-order ordinary differential equation describing the concentration variation associated with diffusion. The model accounts for mass transport and heterogeneous electrochemical reaction. The solution of this model is by the approximate Adomian polynomial method and is used to determine lateral distributions of concentration, overpotential and current density and overall cell polarisation. The model is used to simulate the effects of important system and operating parameters, i.e. local diffusion rates, and mass transport coefficients and electrode polarisation behaviour. [source] ## He's homotopy perturbation method for two-dimensional heat conduction equation: Comparison with finite element method HEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2010M. JalaalAbstract Heat conduction appears in almost all natural and industrial processes. In the current study, a two-dimensional heat conduction equation with different complex Dirichlet boundary conditions has been studied. An analytical solution for the temperature distribution and gradient is derived using the homotopy perturbation method (HPM). Unlike most of previous studies in the field of analytical solution with homotopy-based methods which investigate the ODEs, we focus on the partial differential equation (PDE). Employing the Taylor series, the gained series has been converted to an exact expression describing the temperature distribution in the computational domain. Problems were also solved numerically employing the finite element method (FEM). Analytical and numerical results were compared with each other and excellent agreement was obtained. The present investigation shows the effectiveness of the HPM for the solution of PDEs and represents an exact solution for a practical problem. The mathematical procedure proves that the present mathematical method is much simpler than other analytical techniques due to using a combination of homotopy analysis and classic perturbation method. The current mathematical solution can be used in further analytical and numerical surveys as well as related natural and industrial applications even with complex boundary conditions as a simple accurate technique. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20292 [source] ## Cover Picture: Fabrication of Multicomponent Microsystems by Directed Three-Dimensional Self-Assembly (Adv. Funct. ADVANCED FUNCTIONAL MATERIALS, Issue 5 2005Mater.Abstract Directed three-dimensional self-assembly to assemble and package integrated semiconductor devices is demonstrated by Jacobs and Zheng on p.,732. The self-assembly process uses geometrical shape recognition to identify different components and surface-tension between liquid solder and metal-coated areas to form mechanical and electrical connections. The components (top left) self-assemble in a turbulent flow (center) and form functional multi-component microsystems (bottom right) by sequentially adding parts to the assembly solution. The technique provides, for the first time, a route to enable the realization of three-dimensional heterogeneous microsystems that contain non-identical parts, and connecting them electrically. We have developed a directed self-assembly process for the fabrication of three-dimensional (3D) microsystems that contain non-identical parts and a statistical model that relates the process yield to the process parameters. The self-assembly process uses geometric-shape recognition to identify different components, and surface tension between liquid solder and metal-coated areas to form mechanical and electrical connections. The concept is used to realize self-packaging microsystems that contain non-identical subunits. To enable the realization of microsystems that contain more than two non-identical subunits, sequential self-assembly is introduced, a process that is similar to the formation of heterodimers, heterotrimers, and higher aggregates found in nature, chemistry, and chemical biology. The self-assembly of three-component assemblies is demonstrated by sequentially adding device segments to the assembly solution including two hundred micrometer-sized light-emitting diodes (LEDs) and complementary metal oxide semiconductor (CMOS) integrated circuits. Six hundred AlGaInP/GaAs LED segments self-assembled onto device carriers in two minutes, without defects, and encapsulation units self-assembled onto the LED-carrier assemblies to form a 3D circuit path to operate the final device. The self-assembly process is a well-defined statistical process. The process follows a first-order, non-linear differential equation. The presented model relates the progression of the self-assembly and yield with the process parameters,component population and capture probability,that are defined by the agitation and the component design. [source] ## Laboratory experimental check of a conceptual model for infiltration under complex rainfall patterns HYDROLOGICAL PROCESSES, Issue 3 2006Florisa MeloneAbstract Experimental evidence of the accuracy of the model proposed by Corradini et al. (1997, Journal of Hydrology192: 104,124) for local infiltration,redistribution,reinfiltration in homogeneous soils is given. The model provides infiltration through the time evolution of the soil water content vertical profile, which is described by an ordinary differential equation in any stage of a given rainfall event. A nearly horizontal laboratory slope was used for the experiments performed over both a medium- and a coarse-textured soil. During each experiment characterized by a complex rainfall pattern, the soil water content , at different depths was continuously monitored using the time-domain reflectometry method. Our results indicate that the model simulated the experimental vertical profiles of , accurately, particularly during the infiltration and reinfiltration stages separated by a rainfall hiatus with redistribution of soil water. These results indicate the reliability of the model in computing the local effective rainfall for hydrological response. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Axisymmetric interaction of a rigid disc with a transversely isotropic half-space INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2010Amir Aabbas KatebiAbstract A theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half-space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth-order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed-boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary-layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## Solution of the unsaturated soil moisture equation using repeated transforms INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2001S. G. FityusAbstract An alternative method of solution for the linearized ,theta-based' form of the Richards equation of unsaturated flow is developed in two spatial dimensions. The Laplace and Fourier transformations are employed to reduce the Richards equation to an ordinary differential equation in terms of a transformed moisture content and the transform variables, s and ,. Separate analytic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis-equilibrium. The solutions are assembled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles. Solution techniques are outlined for various boundary conditions including prescribed constant moisture content, prescribed constant flux and flux as a function of moisture change. Example solutions are compared with linearized finite element solutions. The agreement is found to be good. An adaptation of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solutions with some earlier semi-analytical, finite element and finite difference results are also favourable. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## DQEM analysis of out-of-plane deflection of non-prismatic curved beam structures considering the effect of shear deformation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2008Chang-New ChenAbstract The development of differential quadrature element method (DQEM) out-of-plane deflection analysis model of curved non-prismatic beam structures considering the effect of shear deformation was carried out. The DQEM uses the differential quadrature (DQ) to discretize the governing differential equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## An interpolation-based local differential quadrature method to solve partial differential equations using irregularly distributed nodes INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2008Hang MaAbstract To circumvent the constraint in application of the conventional differential quadrature (DQ) method that the solution domain has to be a regular region, an interpolation-based local differential quadrature (LDQ) method is proposed in this paper. Instead of using regular nodes placed on mesh lines in the DQ method (DQM), irregularly distributed nodes are employed in the LDQ method. That is, any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of irregularly distributed nodes in the local physical domain. The feature of the new approach lies in the fact that the weighting coefficients are determined by the quadrature rule over the irregularly distributed local supporting nodes with the aid of nodal interpolation techniques developed in the paper. Because of this distinctive feature, the LDQ method can be consistently applied to linear and nonlinear problems and is really a mesh-free method without the limitation in the solution domain of the conventional DQM. The effectiveness and efficiency of the method are validated by two simple numerical examples by solving boundary-value problems of a linear and a nonlinear partial differential equation. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Numerical procedure for fluid flow in a pipe performing transverse oscillations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2007M. RagulskisAbstract Numerical procedure for the analysis of fluid flow in a tube performing transverse oscillations is developed. The formulation of the problem is presented in differential equation form and a finite element model is developed leading to the first-order matrix differential equation. The fluid flow model incorporates transverse oscillation of the boundary through the convective inertia terms. Modal decomposition of the solution is performed and a technique for numerical solution of the finite element problem incorporating parametric vibrations is developed. Numerical results provide insight into the problem of fluid flow control by transverse vibrations of the tube. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Harmonic balance method for FEM analysis of fluid flow in a vibrating pipe INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2006M. RagulskisAbstract A numerical procedure for the analysis of non-Newtonian fluid flow in a longitudinally vibrating tube is developed. The formulation of the problem is presented in differential equation form and finite element model is developed leading to the first-order matrix differential equation. A special modification of the harmonic balance procedure is proposed for this non-linear problem. Numerical validation of the harmonic balance procedure was performed by comparison of the average mass flow rate with the results of direct time integration. Copyright © 2005 John Wiley & Sons, Ltd. [source] |