Department of Mathematics, Jimma University, Jimma, Ethiopia.
BMC Res Notes. 2021 Dec 11;14(1):446. doi: 10.1186/s13104-021-05858-4.
The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions.
The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology of Mickens procedure is used in the spatial direction and also within the first order temporal direction that construct the first-order finite difference approximation to solve the considered problem numerically. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. Numerical experiments were conducted to support the theoretical results.
本文的主要目的是提出一种加速非标准有限差分方法来求解奇异摄动 Burger-Huxley 方程，以产生更精确的解。
本文采用拟线性化技术将非线性项线性化。在空间方向和一阶时间方向上采用 Mickens 过程的非标准方法构建一阶有限差分逼近，对所考虑的问题进行数值求解。为了加速从一阶到二阶的收敛速度，应用了 Richardson 外推技术。进行了数值实验以支持理论结果。
