Abstract

In this paper, the Lie–Trotter splitting method (LSM) is used to solve the generalized Burgers–Huxley equation (GBHE) numerically. We first establish the local error bounds for approximate solutions of the GBHE with the help of the differential theory of operators in a Banach space. Then we prove the global convergence by using a telescoping identity. In the end, the accuracy of the method is proved by numerical results, which are compared with earlier studies.

中文翻译：

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用 Lie-Trotter 分裂法求解广义 Burgers-Huxley 方程

摘要

在本文中，Lie-Trotter 分裂方法 (LSM) 用于数值求解广义 Burgers-Huxley 方程 (GBHE)。我们首先借助 Banach 空间中算子的微分理论建立 GBHE 近似解的局部误差界。然后我们通过使用伸缩恒等式证明全局收敛。最后，通过数值结果证明了该方法的准确性，并与早期研究进行了比较。