A numerical approach to Caudrey Dodd Gibbon equation via collocation method using quintic b-spline basis

Abstract

In this manuscript, a numerical approach is investigated to Caudrey-DoddGibbon (CDG) equation. The nonlinear CDG equation is reduced to a system of partial differential equation using uxxx = v. The new numerical solutions are obtained with a combination of collocation method with finite element method which is one of the most important methods among all numerical approaches. In order to proceed the method, solution for each unknown is written as a linear combination of time parameters and quintic B-spline basis. Then, with the advantage of the collocation method, a system of algebraic equation systems is formulated easily. Solving the system iteratively by a method results in numerical solutions of the CDG equation. The numerical solutions together with the error norms L₂, L∞ are tabulated. Additionally, graphical simulations of the solutions are depicted by figures.