Purpose

The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients.

Design/methodology/approach

The strictly positive definite radial basis functions collocation method together with the decomposition of the interpolation matrix is used to turn the problem into a system of nonlinear first-order differential equations. Then a numerical solution of this system is computed by changing in the classical fourth-order Runge–Kutta method as well.

Findings

Several test problems are provided to confirm the validity and efficiently of the proposed method.

Originality/value

For the first time, some famous examples are solved by using the proposed high-order technique.

中文翻译：

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SPD-RBF线法在求解非线性变系数对流-扩散-反应方程中的应用

目的

本研究的目的是利用直线法求解变系数的二维非线性对流-扩散-反应方程。

设计/方法/方法

采用严格正定径向基函数搭配方法，结合插值矩阵的分解，将问题转化为非线性一阶微分方程组。然后通过改变经典的四阶 Runge-Kutta 方法来计算该系统的数值解。

发现

提供了几个测试问题来确认所提出方法的有效性和有效性。

原创性/价值

首次使用所提出的高阶技术解决了一些著名的例子。