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Taylor Series (taylor + series)

Distribution by Scientific Domains
Engineering70%

Terms modified by Taylor Series

  • taylor series expansion
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    Selected Abstracts

    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 2010
    M. Jalaal
    Abstract 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]

    Error estimates in 2-node shear-flexible beam elements

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2003
    Gajbir Singh
    Abstract The objective of the paper is to report the investigation of error estimates/or convergence characteristics of shear-flexible beam elements. The order and magnitude of principal discretization error in the usage of various types beam elements such as: (a) 2-node standard isoparametric element, (b) 2-node field-consistent/reduced integration element and (c) 2-node coupled-displacement field element, is assessed herein. The method employs classical order of error analyses that is commonly used to evaluate the discretization error of finite difference methods. The finite element equilibrium equations at any node are expressed in terms of differential equations through the use of Taylor series. These differential equations are compared with the governing equations and error terms are identified. It is shown that the discretization error in coupled-field elements is the least compared to the field-consistent and standard finite elements (based on exact integration). Copyright © 2003 John Wiley & Sons, Ltd. [source]

    A generalized dimension-reduction method for multidimensional integration in stochastic mechanics

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2004
    H. Xu
    Abstract A new, generalized, multivariate dimension-reduction method is presented for calculating statistical moments of the response of mechanical systems subject to uncertainties in loads, material properties, and geometry. The method involves an additive decomposition of an N -dimensional response function into at most S -dimensional functions, where S,N; an approximation of response moments by moments of input random variables; and a moment-based quadrature rule for numerical integration. A new theorem is presented, which provides a convenient means to represent the Taylor series up to a specific dimension without involving any partial derivatives. A complete proof of the theorem is given using two lemmas, also proved in this paper. The proposed method requires neither the calculation of partial derivatives of response, as in commonly used Taylor expansion/perturbation methods, nor the inversion of random matrices, as in the Neumann expansion method. Eight numerical examples involving elementary mathematical functions and solid-mechanics problems illustrate the proposed method. Results indicate that the multivariate dimension-reduction method generates convergent solutions and provides more accurate estimates of statistical moments or multidimensional integration than existing methods, such as first- and second-order Taylor expansion methods, statistically equivalent solutions, quasi-Monte Carlo simulation, and the fully symmetric interpolatory rule. While the accuracy of the dimension-reduction method is comparable to that of the fourth-order Neumann expansion method, a comparison of CPU time suggests that the former is computationally far more efficient than the latter. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    A Taylor series-based finite volume method for the Navier,Stokes equations

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2008
    G. X. Wu
    Abstract A Taylor series-based finite volume formulation has been developed to solve the Navier,Stokes equations. Within each cell, velocity and pressure are obtained from the Taylor expansion at its centre. The derivatives in the expansion are found by applying the Gauss theorem over the cell. The resultant integration over the faces of the cell is calculated from the value at the middle point of the face and its derivatives, which are further obtained from a higher order interpolation based on the values at the centres of two cells sharing this face. The terms up to second order in the velocity and the terms up to first order in pressure in the Taylor expansion are retained throughout the derivation. The test cases for channel flow, flow past a circular cylinder and flow in a collapsible channel have shown that the method is quite accurate and flexible. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Generalized lattice-BGK concept for thermal and chemically reacting flows at low Mach numbers

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006
    D. Hänel
    Abstract The lattice-BGK method has been extended by introducing additional, free parameters in the original formulation of the lattice-BGK methods. The relationship between these parameters and the macroscopic moment equations is analysed by Taylor series and Chapman,Enskog expansion. The parameters are determined from the macroscopic moment equations by comparisons with the governing equations to be modelled. Extensions are presented for the Navier,Stokes equations at low Mach numbers in Cartesian or axisymmetric coordinates with constant or variable density, for scalar convection,diffusion equations and for equations of Poisson type. The generalized lattice-BGK concept is demonstrated by two applications of chemical engineering. These are the computation of chemically reacting flow through an axisymmetric reactor and of the transport and deposition of particles to filters under the action of different forces. Copyright © 2006 John Wiley & Sons, Ltd. [source]

    A posteriori pointwise error estimation for compressible fluid flows using adjoint parameters and Lagrange remainder

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005
    A. K. Alekseev
    Abstract The pointwise error of a finite-difference calculation of supersonic flow is discussed. The local truncation error is determined by a Taylor series with the remainder being in a Lagrange form. The contribution of the local truncation error to the total pointwise approximation error is estimated via adjoint parameters. It is demonstrated by numerical tests that the results of the numerical calculation of gasdynamics parameter at an observation point may be refined and an error bound may be estimated. The results of numerical tests for the case of parabolized Navier,Stokes are presented as an illustration of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Small confidence sets for the mean of a spherically symmetric distribution

    JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2005
    Richard Samworth
    Summary., Suppose that X has a k -variate spherically symmetric distribution with mean vector , and identity covariance matrix. We present two spherical confidence sets for ,, both centred at a positive part Stein estimator . In the first, we obtain the radius by approximating the upper , -point of the sampling distribution of by the first two non-zero terms of its Taylor series about the origin. We can analyse some of the properties of this confidence set and see that it performs well in terms of coverage probability, volume and conditional behaviour. In the second method, we find the radius by using a parametric bootstrap procedure. Here, even greater improvement in terms of volume over the usual confidence set is possible, at the expense of having a less explicit radius function. A real data example is provided, and extensions to the unknown covariance matrix and elliptically symmetric cases are discussed. [source]

    Analytic approximation formulae for pricing forward-starting Asian options

    THE JOURNAL OF FUTURES MARKETS, Issue 5 2003
    Chueh-Yung Tsao
    In this article we first identify a missing term in the Bouaziz, Briys, and Crouhy (1994) pricing formula for forward-starting Asian options and derive the correct one. First, illustrate in certain cases that the missing term in their pricing formula could induce large pricing errors or unreasonable option prices. Second, we derive new analytic approximation formulae for valuing forward-starting Asian options by adding the second-order term in the Taylor series. We show that our formulae can accurately value forward-starting Asian options with a large underlying asset's volatility or a longer time window for the average of the underlying asset prices, whereas the pricing errors for these options with the previously mentioned formula could be large. Third, we derive the hedge ratios for these options and compare their properties with those of plain vanilla options. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:487,516, 2003 [source]

    Empowering surgical nurses improves compliance rates for antibiotic prophylaxis after caesarean birth

    JOURNAL OF ADVANCED NURSING, Issue 11 2009
    Zvi Shimoni
    Abstract Title.,Empowering surgical nurses improves compliance rates for antibiotic prophylaxis after caesarean birth. Aim., This paper is a report of a study of the effect of empowering surgical nurses to ensure that patients receive antibiotic prophylaxis after caesarean birth. Background., Despite the consensus that single dose antibiotic prophylaxis is beneficial for women have either elective or non-elective caesarean delivery, hospitals need methods to increase compliance rates. Method., In a study in Israel in 2007 surgical nurses were empowered to ensure that a single dose of cefazolin was given to the mother after cord clamping. A computerized system was used to identify women having caesarean births, cultures sent and culture results. Compliance was determined by chart review. Rates of compliance, suspected wound infections, and confirmed wound infections in 2007 were compared to rates in 2006 before the policy change. Relative risks were calculated dividing 2007 rates by those in 2006, and 95% confidence intervals were calculated using Taylor's series that does not assume a normal distribution. Statistical significance was assessed using the chi-square test. Findings., The compliance rate was increased from 25% in 2006 to 100% in 2007 (chi-square test, P < 0·001). Suspected wound infection rates decreased from 16·8% (186/1104) to 12·6% (137/1089) after the intervention (relative risk 0·75, 95% confidence interval, 0·61,0·92). Conclusion., Surgical nurses can ensure universal compliance for antibiotic prophylaxis in women after caesarean birth, leading to a reduction in wound infections. [source]