A new method to deduce high-order compact difference schemes for two-dimensional Poisson equation
作者： Shuying Zhai , Xinlong Feng , Yinnian He
DOI: 10.1016/J.AMC.2013.12.096
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摘要: Abstract This paper introduces a novel method for deducing high-order compact difference schemes the two-dimensional (2D) Poisson equation. Like finite volume method, dual partition is introduced. Combining Simpson integral formula and parabolic interpolation, family of fourth-order sixth-order are obtained based on three different types partitions. Moreover, several new gained numerical experiments shown two them much better than almost any other which have been presented in others’ work. The outline nonlinear equation also given. Numerical to verify feasibility this high accuracy these schemes.
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Kun Wang, Xinlong Feng, New predictor-corrector methods of second-order for solving nonlinear equations International Journal of Computer Mathematics. ,vol. 88, pp. 296- 313 ,(2011) , 10.1080/00207160903443748
R.K. Mohanty, Swarn Singh, A new fourth order discretization for singularly perturbed two dimensional non-linear elliptic boundary value problems Applied Mathematics and Computation. ,vol. 175, pp. 1400- 1414 ,(2006) , 10.1016/J.AMC.2005.08.023
Haiwei Sun, Jun Zhang, A high‐order finite difference discretization strategy based on extrapolation for convection diffusion equations Numerical Methods for Partial Differential Equations. ,vol. 20, pp. 18- 32 ,(2004) , 10.1002/NUM.10075
Jun Zhang, Multigrid Method and Fourth-Order Compact Scheme for 2D Poisson Equation with Unequal Mesh-Size Discretization Journal of Computational Physics. ,vol. 179, pp. 170- 179 ,(2002) , 10.1006/JCPH.2002.7049
R. Manohar, J. W. Stephenson, Optimal Finite Analytic Methods Journal of Heat Transfer. ,vol. 104, pp. 432- 437 ,(1982) , 10.1115/1.3245111
Xinlong Feng, Rongfei Li, Yinnian He, Demin Liu, P 1 -Nonconforming Quadrilateral Finite Volume Methods for the Semilinear Elliptic Equations Journal of Scientific Computing. ,vol. 52, pp. 519- 545 ,(2012) , 10.1007/S10915-011-9557-4
G. W. Hedstrom, G. D. Smith, Numerical Solution of Partial Differential Equations. American Mathematical Monthly. ,vol. 73, pp. 1140- ,(1966) , 10.2307/2314674
R. Manohar, J. W. Stephenson, High Order Difference Shemes for Linear Partial Differential Equations SIAM Journal on Scientific and Statistical Computing. ,vol. 5, pp. 69- 77 ,(1984) , 10.1137/0905005
Karthik Balakrishnan, Palghat A. Ramachandran, Osculatory interpolation in the method of fundamental solution for nonlinear Poisson problems Journal of Computational Physics. ,vol. 172, pp. 1- 18 ,(2001) , 10.1006/JCPH.2001.6796
Robert Edward Lynch, Garrett Birkhoff, Numerical Solution of Elliptic Problems ,(1984)