Subdivision collocation method: a new numerical technique for solving hyperbolic partial differential equation in non-uniform medium

Abstract

This paper deals with a new numerical technique for solving the second order linear homogeneous and inhomogeneous hyperbolic partial differential equation with variable and constant coefficients. In this technique, the time derivative is described using a finite difference technique, while the collocation method based on subdivision scheme is used to interpose the space dimension. The convergence and error estimation of the proposed technique along with comparison have been presented in this paper. In terms of computational efficiency, our technique yields a solution that is identical to existing works. Furthermore, the applicability and effectiveness of proposed technique are illustrated with numerical examples.