A meshless two-stage scheme for the fifth-order dispersive models in the science of waves on water. (15th April 2022) - Seydaoğlu, M.
Abstract: In this study, we investigate the numerical solution of the higher odd-order PDEs, called the Kawahara and Kawahara-KdV equations, which are main models to study the dynamics of water waves. We combine the two-stage fourth order exponential Rosenbrock integrator with a meshfree scheme based on multiquadric-radial basis function (MQ-RBF) in time and space discretization, respectively. We demonstrate the scheme based on this combination for two test examples of the Kawahara-type dispersive equations with their solitary wave solutions. The obtained results are compared with the previous findings and are figured out graphically. It is shown that the proposed algorithm provides compatible and higher accurate results in order to efficiently illustrate the behavior of solitary waves. Highlights: A new numerical scheme is employed to solve models in the science of water on waves. The meshless RBFs technique has been combined with the two-stage exponential Rosenbrock method to tailor a new numerical algorithm. The tailored method has been performed to approximate some important examples of the Kawahara-type equations. The scheme is able to display correct physical dynamics of the problems including dispersive and dissipative terms.