The B-spline Collocation Approach for Coupled Klein-Gordon Equation

Abstract

This research presents a new approach for obtaining numerical solutions of Coupled Klein Gordon equation using the collocation method which based on cubic B-spline base functions and finite element approximation. The main advantage of the collocation method is that the structure of the method is simple and the computational cost is low. It also provides an easy and simpler procedure for solving various problems involving differential equations that model real-world phenomena . In the current research, the temporal and spatial partial derivatives are discretized with using approximate solution which is formed linear combination of B-spline basis and time dependent parameters. With the help of the idea that approximate solution satisfy the PDE at collocation points, a new numerical scheme is constructed. The newly obtained numerical scheme tested on a model problem. Numerical results are compared with exact solution with the aid of the error norms L 2 and L s presented via tables . Additionally, graphical simulations of numerical solutions are presented.