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High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

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  • Yan Wang
  • Yongbin Ge

Abstract

A high-order compact difference scheme for solving the two-dimensional (2D) elliptic problems is proposed by including compact approximations to the leading truncation error terms of the central difference scheme. A multigrid method is employed to overcome the difficulties caused by conventional iterative methods when they are used to solve the linear algebraic system arising from the high-order compact scheme. Numerical experiments are conducted to test the accuracy and efficiency of the present method. The computed results indicate that the present scheme achieves the fourth-order accuracy and the effect of the multigrid method for accelerating the convergence speed is significant.

Suggested Citation

  • Yan Wang & Yongbin Ge, 2018. "High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-11, June.
    • Handle: RePEc:hin:jnlmpe:7831731
    DOI: 10.1155/2018/7831731
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    Cited by:

    1. Lili Wu & Xiufang Feng, 2019. "A High-Order Compact (HOC) Implicit Difference Scheme and a Multigrid Method for Solving 3D Unsteady Reaction Diffusion Equations," Mathematics, MDPI, vol. 7(12), pages 1-11, December.

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