Cubic B-spline quasi-interpolation and an application to numerical solution of generalized Burgers-Huxley equation
Cubic B-spline quasi-interpolation and an application to numerical solution of generalized Burgers-Huxley equation
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DOI：
10.1177/1687814020971061
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发表时间：
2020-11
影响因子：
2.1
通讯作者：
Lan-Yin Sun;Chungang Zhu
中科院分区：
文献类型：
--
作者：
Lan-Yin Sun;Chungang Zhu
非线性偏微分方程组在应用数学和物理学中得到了广泛的研究。广义Burgers-Huxley方程在不同的非线性物理机制中起着重要的作用。本文提出了一种用于求解Burgers-Huxley方程的三次B-Spline拟插值法。首先，提出了三次B-样条拟插值法。然后，用拟内插的导数逼近因变量的空间导数，用修正的欧拉格式逼近因变量的时间导数，得到数值格式。数值解与解析解的一致性说明了所提方法的有效性，表明数值格式是可以接受的。
Nonlinear partial differential equations are widely studied in Applied Mathematics and Physics. The generalized Burgers-Huxley equations play important roles in different nonlinear physics mechanisms. In this paper, we develop a kind of cubic B-spline quasi-interpolation which is used to solve Burgers-Huxley equations. Firstly, the cubic B-spline quasi-interpolation is presented. Next we get the numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and modified Euler scheme to approximate the time derivative of the dependent variable. Moreover, the efficiency of the proposed method is illustrated by the agreement between the numerical solution and the analytical solution which indicate the numerical scheme is quite acceptable.