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

Yueyue Pan, Lifei Wu and Xiaozhong Yang

Mathematical Problems in Engineering, 2020, vol. 2020, 1-17

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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:9162563

DOI: 10.1155/2020/9162563

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