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

Abstract

PurposeThe 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/approachThe 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.FindingsSeveral test problems are provided to confirm the validity and efficiently of the proposed method.Originality/valueFor the first time, some famous examples are solved by using the proposed high-order technique.