A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation

Author:

Pan Yueyue1ORCID,Wu Lifei2ORCID,Yang Xiaozhong2ORCID

Affiliation:

1. School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China

2. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China

Abstract

This paper proposes a new class of difference methods with intrinsic parallelism for solving the Burgers–Fisher equation. A new class of parallel difference schemes of pure alternating segment explicit-implicit (PASE-I) and pure alternating segment implicit-explicit (PASI-E) are constructed by taking simple classical explicit and implicit schemes, combined with the alternating segment technique. The existence, uniqueness, linear absolute stability, and convergence for the solutions of PASE-I and PASI-E schemes are well illustrated. Both theoretical analysis and numerical experiments show that PASE-I and PASI-E schemes are linearly absolute stable, with 2-order time accuracy and 2-order spatial accuracy. Compared with the implicit scheme and the Crank–Nicolson (C-N) scheme, the computational efficiency of the PASE-I (PASI-E) scheme is greatly improved. The PASE-I and PASI-E schemes have obvious parallel computing properties, which show that the difference methods with intrinsic parallelism in this paper are feasible to solve the Burgers–Fisher equation.

Funder

Subproject of Major Science and Technology Program of China

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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