Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients

Abstract

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.

Citation

Mesgarani, H., Kermani, M. and Abbaszadeh, M. (2022), "Application of SPD-RBF method of lines for solving nonlinear advection–diffusion–reaction equation with variable coefficients", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 2, pp. 850-886. https://doi.org/10.1108/HFF-07-2020-0459