A combined meshfree exponential Rosenbrock integrator for the third-order dispersive partial differential equations

Abstract

The aim of this study is to propose a combined numerical treatment for the dispersive partial differential equations involving dissipation, convection and reaction terms with nonlinearity, such as the KdV-Burgers, KdV and dispersive-Fisher equations. We use the combination of the exponential Rosenbrock–Euler time integrator and multiquadric-radial basis function meshfree scheme in space as a qualitatively promising and computationally inexpensive method to efficiently exhibit behavior of such fruitful interactions resulting in antikink, two solitons and antikink-breather waves. Obtained numerical solutions are compared with the existing results in the literature and discussed using illustrations in detail. © 2020 Wiley Periodicals LLC