A New Class of Difference Methods with Intrinsic Parallelism for Burgers–Fisher Equation
| Autor: | Yueyue Pan, Lifei Wu, Xiaozhong Yang |
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| Rok vydání: | 2020 |
| Předmět: |
Article Subject
General Mathematics General Engineering Fisher equation 010103 numerical & computational mathematics Engineering (General). Civil engineering (General) 01 natural sciences 010101 applied mathematics Simple (abstract algebra) Scheme (mathematics) Convergence (routing) QA1-939 Parallelism (grammar) Applied mathematics Uniqueness TA1-2040 0101 mathematics Absolute stability Mathematics |
| Zdroj: | Mathematical Problems in Engineering, Vol 2020 (2020) |
| ISSN: | 1563-5147 1024-123X |
| DOI: | 10.1155/2020/9162563 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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