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R. H. Li, B. Liu. The numerical solutions of partial differential equation (3rd Edition). Beijing: Higher Education Press. 2009:107-149. (In Chinese)


  • 标题: 并行求解抛物型偏微分方程的一种新ASE-I格式 A New ASE-I Method for Solving Parabolic Equations

    作者: 王栋, 冯蕾

    关键字: 抛物型方程, 差分格式, 并行算法 Parabolicl Equations; Parallel Algorithm; Difference Scheme

    期刊名称: 《Advances in Applied Mathematics》, Vol.2 No.1, 2013-02-26

    摘要: 通过古典显、隐格式和Saul’yev非对称格式,本文构造了一种并行求解抛物型偏微分方程的一种新的ASE-I格式。这种新的差分格式兼具绝对稳定性和高度并行性,并且分段更加灵活,从而这种新的差分格式应用更加广泛。本文给出这种新的差分格式的数学形式,分析了稳定性并得出了稳定性定理。最后通过数值算例验证了这种新ASE-I格式的稳定性和精确性,数值试验结果和理论分析相符合。In this paper, I construct a new ASE-I scheme for solving parabolic partial differential equations in parallel through classical explicit-implicit format and the Saul’yev asymmetric formats. This method is absolutely parallel and stable, and the sub-sections are more flexible, so the scheme is more convenient to apply to solve parabolic partial differential equations. In this paper, we list the mathematical form of this finite difference scheme, analyze the stability of the scheme, and verify the stability and accuracy of this scheme through numerical experiments. The results of numerical experiments are consistent with the theoretical analysis.