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

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. [ABSTRACT FROM AUTHOR]