High accuracy explicit compact difference scheme for the diffusion equation

doi:10.3969/j.issn.1000-1565.2016.02.002

Abstract

Abstract: Based on the fourth-order compact difference formula of the second-order derivative in spatial direction and Taylor series expansion in time direction,a high-order explicit compact difference scheme for the one dimentional diffusion equation is developed.The stability of the scheme is analyzed by Fourier method,and the condition of stability is λ≤1/2(λ is the mesh ratio).Numerical experiments are carried out to verify the accuracy and reliability of the present scheme.

Key words: diffusion equation, high accuracy, compact scheme, explicit scheme, finite difference method

CLC Number:

O241.82

YANG Xiaojia,WANG Yan. High accuracy explicit compact difference scheme for the diffusion equation[J]. Journal of Hebei University (Natural Science Edition), 2016, 36(2): 117-123.

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