A One-Step Block Hybrid Integrator for Solving Fifth Order Korteweg-de Vries Equations

Abstract

Fifth-order Korteweg-de Vries (KdV) equations, arise in modeling waves phenomena such as the propagation of shallow water waves over a flat surface, gravity-capillary waves and sound waves in plasmas. In this work, a one-step block hybrid linear multistep method was derived using the collocation technique, to solve fifth-order KdV models via the Method of Line (MoL). The consistency, stability and convergence of the method were established. The efficiency of the method can be seen from comparison of the exact solutions of problems and other methods cited from literature.

Keywords

• Korteweg-de Vries (KdV) equations, Fifth-order PDE, Linear multistep, Block Method, Convergence