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## Approximate Solution (approximate + solution)
## Selected Abstracts## Approximate solution of the Takagi,Taupin equations for a semi-infinite crystal in the three-beam Laue,Laue case ACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2001Gunnar ThorkildsenAn analytical approximate solution of the Takagi,Taupin equations for a symmetrical three-beam Laue,Laue case in a perfect non-absorbing semi-infinite crystal slab has been obtained. The expression, a second-order expansion, is valid for situations where the effective crystal thickness does not exceed half the actual extinction length and it is shown to be in perfect agreement with the full numerical solution of the fundamental equations. [source] ## Balanced boundary layers used in hurricane models THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 635 2008Roger K. SmithAbstract We examine the formulation and accuracy of various approximations made in representing the boundary layer in simple axisymmetric hurricane models, especially those that assume strict gradient wind balance in the radial direction. Approximate solutions for a steady axisymmetric slab boundary-layer model are compared with a full model solution. It is shown that the approximate solutions are generally poor in the inner core region of the vortex, where the radial advection term in the radial momentum equation is important and cannot be neglected. These results affirm some prior work and have implications for a range of theoretical studies of hurricane dynamics, including theories of potential intensity, that employ balanced boundary-layer formulations. Copyright © 2008 Royal Meteorological Society [source] ## The Development of New Analytic Elements for Transient Flow and Multiaquifer Flow GROUND WATER, Issue 1 2006O.D.L. StrackWe deal in this paper with an ongoing development of the analytic element method. We present in outline new analytic line elements that are suitable to model general flow fields, i.e., flow fields that possess a continuously varying areal inflow or outflow. These elements are constructed specifically to model the leakage through leaky layers that separate aquifers in leaky systems and to model transient effects. The leakage or release from storage underneath linear features is modeled precisely by the new elements; the singularity in leakage is matched exactly by the approximate solution. Applications are given for a problem involving leakage and for a case of transient flow. We note that the analytic elements can be used also to reproduce the effect of continuously varying aquifer properties, e.g., the hydraulic conductivity or the elevation of the base of the aquifer. In the latter case, the elements would reproduce the rotation of the flow field caused by the variation in properties, rather than the divergence as for the case of leakage. [source] ## Approximate discharge for constant head test with recharging boundary GROUND WATER, Issue 3 2005Philippe RenardThe calculation of the discharge to a constant drawdown well or tunnel in the presence of an infinite linear constant head boundary in an ideal confined aquifer usually relies on the numerical inversion of a Laplace transform solution. Such a solution is used to interpret constant head tests in wells or to roughly estimate ground water inflow into tunnels. In this paper, a simple approximate solution is proposed. Its maximum relative error is on the order of 2% as compared to the exact analytical solution. The approximation is a weighted mean between the early-time and late-time asymptotes. [source] ## Modelling of contaminant transport through landfill liners using EFGM INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010R. Praveen KumarAbstract Modelling of contaminant transport through landfill liners and natural soil deposits is an important area of research activity in geoenvironmental engineering. Conventional mesh-based numerical methods depend on mesh/grid size and element connectivity and possess some difficulties when dealing with advection-dominant transport problems. In the present investigation, an attempt has been made to provide a simple but sufficiently accurate methodology for numerical simulation of the two-dimensional contaminant transport through the saturated homogeneous porous media and landfill liners using element-free Galerkin method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The EFGM employs moving least-square approximants to approximate the function and uses the Lagrange multiplier method for imposing essential boundary conditions. The results of the EFGM are validated using experimental results. Analytical and finite element solutions are also used to compare the results of the EFGM. In order to test the practical applicability and performance of the EFGM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the EFGM and the field investigation data. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010A. NouyAbstract An eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial differential equations defined on random domains. This method is based on a marriage between the eXtended Finite Element Method and spectral stochastic methods. In this article, we propose an extension of this method for the numerical simulation of random multi-phased materials. The random geometry of material interfaces is described implicitly by using random level set functions. A fixed deterministic finite element mesh, which is not conforming to the random interfaces, is then introduced in order to approximate the geometry and the solution. Classical spectral stochastic finite element approximation spaces are not able to capture the irregularities of the solution field with respect to spatial and stochastic variables, which leads to a deterioration of the accuracy and convergence properties of the approximate solution. In order to recover optimal convergence properties of the approximation, we propose an extension of the partition of unity method to the spectral stochastic framework. This technique allows the enrichment of approximation spaces with suitable functions based on an a priori knowledge of the irregularities in the solution. Numerical examples illustrate the efficiency of the proposed method and demonstrate the relevance of the enrichment procedure. Copyright © 2010 John Wiley & Sons, Ltd. [source] ## Large-scale parallel finite-element analysis using the internet: a performance study INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005Ryuji ShioyaAbstract This paper describes a parallel finite-element system implemented using the domain decomposition method on a cluster of remote computers connected via the Internet. This technique is also readily applicable to a grid computing environment. A three-dimensional finite-element elastic analysis involving more than one million degrees of freedom was solved using this system, and a good approximate solution was obtained with high parallel efficiency of over 90% using remote computers located in three different countries. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Time-dependent heat transfer coefficient of a wall INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 9 2003Periklis E. ErgatisAbstract A time-dependent coefficient of heat transfer is proposed for the computation of thermal power required, so that a room temperature reaches a desired value within a given time. A mathematical formulation of the room heating transient phenomenon is constructed in a dimensionless form. Using an integral approximate solution an analytical expression for this coefficient is provided and it is verified by diagrams adopted by DIN 4701. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## MAP fusion method for superresolution of images with locally varying pixel quality INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 4 2008Kio KimAbstract Superresolution is a procedure that produces a high-resolution image from a set of low-resolution images. Many of superresolution techniques are designed for optical cameras, which produce pixel values of well-defined uncertainty, while there are still various imaging modalities for which the uncertainty of the images is difficult to control. To construct a superresolution image from low-resolution images with varying uncertainty, one needs to keep track of the uncertainty values in addition to the pixel values. In this paper, we develop a probabilistic approach to superresolution to address the problem of varying uncertainty. As direct computation of the analytic solution for the superresolution problem is difficult, we suggest a novel algorithm for computing the approximate solution. As this algorithm is a noniterative method based on Kalman filter-like recursion relations, there is a potential for real-time implementation of the algorithm. To show the efficiency of our method, we apply this algorithm to a video sequence acquired by a forward looking sonar system. © 2008 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 18, 242,250, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). [source] ## Design of nonlinear observers with approximately linear error dynamics using multivariable Legendre polynomials INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 15 2006Joachim DeutscherAbstract This paper presents a numerical approach to the design of nonlinear observers by approximate error linearization. By using a Galerkin approach on the basis of multivariable Legendre polynomials an approximate solution to the singular PDE of the observer design technique proposed by Kazantzis and Krener (see (Syst. Control Lett. 1998; 34:241,247; SIAM J. Control Optim. 2002; 41:932,953)) is determined. It is shown that the L2 -norm of the remaining nonlinearity in the resulting error dynamics can be made small on a specified multivariable interval in the state space. Furthermore, a linear matrix equation is derived for determining the corresponding change of co-ordinates and output injection such that the proposed design procedure can easily be implemented in a numerical software package. A simple example demonstrates the properties of the new numerical observer design. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Crystallization Kinetics and Electrical Relaxation of BaO,0.5Li2O,4.5B2O3 Glasses JOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 9 2009Rahul VaishTransparent glasses in the composition BaO,0.5Li2O,4.5B2O3 (BLBO) were fabricated via the conventional melt-quenching technique. X-ray powder diffraction combined with differential scanning calorimetric (DSC) studies carried out on the as-quenched samples confirmed their amorphous and glassy nature, respectively. The crystallization behavior of these glasses has been studied by isothermal and nonisothermal methods using DSC. Crystallization kinetic parameters were evaluated from the Johnson,Mehl,Avrami equation. The value of the Avrami exponent (n) was found to be 3.6±0.1, suggesting that the process involves three-dimensional bulk crystallization. The average value of activation energy associated with the crystallization of BLBO glasses was 317±10 kJ/mol. Transparent glass,ceramics were fabricated by controlled heat-treatment of the as-quenched glasses at 845 K/40 min. The dielectric constants for BLBO glasses and glass,ceramics in the 100 Hz,10 MHz frequency range were measured as a function of the temperature (300,925 K). The electrical relaxation and dc conductivity characteristics were rationalized using electric modulus formalism. The imaginary part of the electric modulus spectra was modeled using an approximate solution of the Kohlrausch,Williams,Watts relation. The temperature-dependent behavior of stretched exponent (,) was discussed for the as-quenched and heat-treated BLBO glasses. [source] ## Joint additive Kullback,Leibler residual minimization and regularization for linear inverse problems MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2007Elena ResmeritaAbstract For the approximate solution of ill-posed inverse problems, the formulation of a regularization functional involves two separate decisions: the choice of the residual minimizer and the choice of the regularizor. In this paper, the Kullback,Leibler functional is used for both. The resulting regularization method can solve problems for which the operator and the observational data are positive along with the solution, as occur in many inverse problem applications. Here, existence, uniqueness, convergence and stability for the regularization approximations are established under quite natural regularity conditions. Convergence rates are obtained by using an a priori strategy. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Simulation of Rayleigh waves in cracked plates MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007M. T. CaoAbstract The aim of this paper is to develop new numerical procedures to detect micro cracks, or superficial imperfections, in thin plates using excitation by Rayleigh waves. We shall consider a unilateral contact problem between the two sides of the crack in an elastic plate subjected to suitable boundary conditions in order to reproduce a single Rayleigh wave cycle. An approximate solution of this problem will be calculated by using one of the Newmark methods for time discretization and a finite element method for space discretization. To deal with the nonlinearity due to the contact condition, an iterative algorithm involving one multiplier will be used; this multiplier will be approximated by using Newton's techniques. Finally, we will show numerical simulations for both cracked and non-cracked plates. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Numerical simulation of the non-linear crack problem with non-penetration MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2004Victor A. KovtunenkoAbstract Here the numerical simulation of some plane Lamé problem with a rectilinear crack under non-penetration condition is presented. The corresponding solids are assumed to be isotropic and homogeneous as well as bonded. The non-linear crack problem is formulated as a variational inequality. We use penalty iteration and the finite-element method to calculate numerically its approximate solution. Applying analytic formulas obtained from shape sensitivity analysis, we calculate then energetic and stress characteristics of the solution, and describe the quasistatic propagation of the crack under linear loading. The results are presented in comparison with the classical, linear crack problem, when interpenetration between the crack faces may occur. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## A regularization procedure for the auto-correlation equation MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2001L. Von WolfersdorfThe paper deals with the auto-correlation equation and its regularization by means of a Lavrent'ev regularization procedure in L2. The solution of this quadratic integral equation of the first kind and of the regularized equation of the second kind are obtained by reduction to a boundary value problem for the Fourier transform of the solution. We prove convergence of the approximate solution to the exact solution and derive a stability estimate for the error. Copyright © John Wiley & Sons, Ltd. [source] ## SOLVING DYNAMIC WILDLIFE RESOURCE OPTIMIZATION PROBLEMS USING REINFORCEMENT LEARNING NATURAL RESOURCE MODELING, Issue 1 2005CHRISTOPHER J. FONNESBECKABSTRACT. An important technical component of natural resource management, particularly in an adaptive management context, is optimization. This is used to select the most appropriate management strategy, given a model of the system and all relevant available information. For dynamic resource systems, dynamic programming has been the de facto standard for deriving optimal state-specific management strategies. Though effective for small-dimension problems, dynamic programming is incapable of providing solutions to larger problems, even with modern microcomputing technology. Reinforcement learning is an alternative, related procedure for deriving optimal management strategies, based on stochastic approximation. It is an iterative process that improves estimates of the value of state-specific actions based in interactions with a system, or model thereof. Applications of reinforcement learning in the field of artificial intelligence have illustrated its ability to yield near-optimal strategies for very complex model systems, highlighting the potential utility of this method for ecological and natural resource management problems, which tend to be of high dimension. I describe the concept of reinforcement learning and its approach of estimating optimal strategies by temporal difference learning. I then illustrate the application of this method using a simple, well-known case study of Anderson [1975], and compare the reinforcement learning results with those of dynamic programming. Though a globally-optimal strategy is not discovered, it performs very well relative to the dynamic programming strategy, based on simulated cumulative objective return. I suggest that reinforcement learning be applied to relatively complex problems where an approximate solution to a realistic model is preferable to an exact answer to an oversimplified model. [source] ## A generalization of the weighted set covering problem NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2005Jian YangAbstract We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b -matching problem. In general, we may use a polynomial-time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256,278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383,390], and V. Chvatal [A greedy heuristic for the set-covering problem, Math Oper Res 4(3) (1979), 233,235] to get an approximate solution for the problem. We find a worst-case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005 [source] ## Backward perturbation analysis for scaled total least-squares problems NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 8 2009X.-W. ChangAbstract The scaled total least-squares (STLS) method unifies the ordinary least-squares (OLS), the total least-squares (TLS), and the data least-squares (DLS) methods. In this paper we perform a backward perturbation analysis of the STLS problem. This also unifies the backward perturbation analyses of the OLS, TLS and DLS problems. We derive an expression for an extended minimal backward error of the STLS problem. This is an asymptotically tight lower bound on the true minimal backward error. If the given approximate solution is close enough to the true STLS solution (as is the goal in practice), then the extended minimal backward error is in fact the minimal backward error. Since the extended minimal backward error is expensive to compute directly, we present a lower bound on it as well as an asymptotic estimate for it, both of which can be computed or estimated more efficiently. Our numerical examples suggest that the lower bound gives good order of magnitude approximations, while the asymptotic estimate is an excellent estimate. We show how to use our results to easily obtain the corresponding results for the OLS and DLS problems in the literature. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## A modified modulus method for symmetric positive-definite linear complementarity problems NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2009Jun-Liang DongAbstract By reformulating the linear complementarity problem into a new equivalent fixed-point equation, we deduce a modified modulus method, which is a generalization of the classical one. Convergence for this new method and the optima of the parameter involved are analyzed. Then, an inexact iteration process for this new method is presented, which adopts some kind of iterative methods for determining an approximate solution to each system of linear equations involved in the outer iteration. Global convergence for this inexact modulus method and two specific implementations for the inner iterations are discussed. Numerical results show that our new methods are more efficient than the classical one under suitable conditions. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Linear system solution by null-space approximation and projection (SNAP) NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 1 2007M. IliAbstract Solutions of large sparse linear systems of equations are usually obtained iteratively by constructing a smaller dimensional subspace such as a Krylov subspace. The convergence of these methods is sometimes hampered by the presence of small eigenvalues, in which case, some form of deflation can help improve convergence. The method presented in this paper enables the solution to be approximated by focusing the attention directly on the ,small' eigenspace (,singular vector' space). It is based on embedding the solution of the linear system within the eigenvalue problem (singular value problem) in order to facilitate the direct use of methods such as implicitly restarted Arnoldi or Jacobi,Davidson for the linear system solution. The proposed method, called ,solution by null-space approximation and projection' (SNAP), differs from other similar approaches in that it converts the non-homogeneous system into a homogeneous one by constructing an annihilator of the right-hand side. The solution then lies in the null space of the resulting matrix. We examine the construction of a sequence of approximate null spaces using a Jacobi,Davidson style singular value decomposition method, called restarted SNAP-JD, from which an approximate solution can be obtained. Relevant theory is discussed and the method is illustrated by numerical examples where SNAP is compared with both GMRES and GMRES-IR. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Application of adapted homotopy perturbation method for approximate solution of Henon-Heiles system NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2010Filiz TaAbstract We performed adapted homotopy perturbation method on the Henon-Heiles system with the help of the symbolic computation of package Maple 10 (User Manual by Maplesoft. www.maplesoft.com). We obtained a new approximate solution of the Henon-Heiles system. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source] ## Bernstein Ritz-Galerkin method for solving an initial-boundary value problem that combines Neumann and integral condition for the wave equation NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2010S.A. YousefiAbstract In this article, the Ritz-Galerkin method in Bernstein polynomial basis is implemented to give an approximate solution of a hyperbolic partial differential equation with an integral condition. We will deal here with a type of nonlocal boundary value problem, that is, the solution of a hyperbolic partial differential equation with a nonlocal boundary specification. The nonlocal conditions arise mainly when the data on the boundary cannot be measured directly. The properties of Bernstein polynomial and Ritz-Galerkin method are first presented, then Ritz-Galerkin method is used to reduce the given hyperbolic partial differential equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique presented in this article. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] ## An upwind finite volume element method based on quadrilateral meshes for nonlinear convection-diffusion problems NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2009Fu-Zheng GaoAbstract Considering an upwind finite volume element method based on convex quadrilateral meshes for computing nonlinear convection-diffusion problems, some techniques, such as calculus of variations, commutating operator, and the theory of prior error estimates and techniques, are adopted. Discrete maximum principle and optimal-order error estimates in H1 norm for fully discrete method are derived to determine the errors in the approximate solution. Thus, the well-known problem [(Li et al., Generalized difference methods for differential equations: numerical analysis of finite volume methods, Marcel Dekker, New York, 2000), p 365.] has been solved. Some numerical experiments show that the method is a very effective engineering computing method for avoiding numerical dispersion and nonphysical oscillations. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009 [source] ## An approximation to the solution of telegraph equation by variational iteration method NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2009J. BiazarAbstract The variational iteration method (VIM) has been applied to solve many functional equations. In this article, this method is applied to obtain an approximate solution for the Telegraph equation. Some examples are presented to show the ability of the proposed method. The results of applying VIM are exactly the same as those obtained by Adomian decomposition method. It seems less computation is needed in proposed method.© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] ## A marker method for the solution of the damped Burgers' equation NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2006Jerome L. V. LewandowskiAbstract A new method for the solution of the damped Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 [source] ## Anisotropic mesh adaptation for numerical solution of boundary value problems NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2004Vít DolejAbstract We present an efficient mesh adaptation algorithm that can be successfully applied to numerical solutions of a wide range of 2D problems of physics and engineering described by partial differential equations. We are interested in the numerical solution of a general boundary value problem discretized on triangular grids. We formulate a necessary condition for properties of the triangulation on which the discretization error is below the prescribed tolerance and control this necessary condition by the interpolation error. For a sufficiently smooth function, we recall the strategy how to construct the mesh on which the interpolation error is below the prescribed tolerance. Solving the boundary value problem we apply this strategy to the smoothed approximate solution. The novelty of the method lies in the smoothing procedure that, followed by the anisotropic mesh adaptation (AMA) algorithm, leads to the significant improvement of numerical results. We apply AMA to the numerical solution of an elliptic equation where the exact solution is known and demonstrate practical aspects of the adaptation procedure: how to control the ratio between the longest and the shortest edge of the triangulation and how to control the transition of the coarsest part of the mesh to the finest one if the two length scales of all the triangles are clearly different. An example of the use of AMA for the physically relevant numerical simulation of a geometrically challenging industrial problem (inviscid transonic flow around NACA0012 profile) is presented. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. [source] ## Approximation of time-dependent, viscoelastic fluid flow: Crank-Nicolson, finite element approximation, NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2004Vincent J. ErvinAbstract In this article we analyze a fully discrete approximation to the time dependent viscoelasticity equations with an Oldroyd B constitutive equation in ,, = 2, 3. We use a Crank-Nicolson discretization for the time derivatives. At each time level a linear system of equations is solved. To resolve the nonlinearities we use a three-step extrapolation for the prediction of the velocity and stress at the new time level. The approximation is stabilized by using a discontinuous Galerkin approximation for the constitutive equation. For the mesh parameter, h, and the temporal step size, ,t, sufficiently small and satisfying ,t , Ch, existence of the approximate solution is proven. A priori error estimates for the approximation in terms of ,t and h are also derived. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 248,283, 2004 [source] ## The upwind finite difference fractional steps methods for two-phase compressible flow in porous media NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2003Yirang YuanAbstract The upwind finite difference fractional steps methods are put forward for the two-phase compressible displacement problem. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high-order difference operators, and prior estimates, are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of seawater intrusion and migration-accumulation of oil resources. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 67,88, 2003 [source] ## A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2001Danping YangAbstract A miscible displacement of one compressible fluid by another in a porous medium is governed by a nonlinear parabolic system. A new mixed finite element method, in which the mixed element system is symmetric positive definite and the flux equation is separated from pressure equation, is introduced to solve the pressure equation of parabolic type, and a standard Galerkin method is used to treat the convection-diffusion equation of concentration of one of the fluids. The convergence of the approximate solution with an optimal accuracy in L2 -norm is proved. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 229,249, 2001 [source] ## dsoa: The implementation of a dynamic system optimization algorithm OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2010Brian C. FabienAbstract This paper describes the ANSI C/C++ computer program dsoa, which implements an algorithm for the approximate solution of dynamics system optimization problems. The algorithm is a direct method that can be applied to the optimization of dynamic systems described by index-1 differential-algebraic equations (DAEs). The types of problems considered include optimal control problems and parameter identification problems. The numerical techniques are employed to transform the dynamic system optimization problem into a parameter optimization problem by: (i) parameterizing the control input as piecewise constant on a fixed mesh, and (ii) approximating the DAEs using a linearly implicit Runge-Kutta method. The resultant nonlinear programming (NLP) problem is solved via a sequential quadratic programming technique. The program dsoa is evaluated using 83 nontrivial optimal control problems that have appeared in the literature. Here we compare the performance of the algorithm using two different NLP problem solvers, and two techniques for computing the derivatives of the functions that define the problem. Copyright © 2009 John Wiley & Sons, Ltd. [source] |