A New Numerical Method Based on Non-Polynomial Spline in Tension Approximations for 1D Quasilinear Hyperbolic Equations on a Variable Mesh

Abstract

In this paper, we derive a new three level implicit method of order two in time and three in space, based on spline in tension approximation for the numerical solution of one space dimensional quasi-linear second order hyperbolic partial differential equation on a variable mesh. We also study application of the proposed method to wave equation in polar coordinates. High order approximation at first time level is briefly discussed which is applicable to solve problems both on uniform and non-uniform mesh. Numerical results are given to illustrate the usefulness of the proposed method.