Cubic Spline Method for 1D Wave Equation in Polar Coordinates

Abstract

Using nonpolynomial cubic spline approximation in space and finite difference in time direction, we discuss three-level implicit difference scheme of O ( k 2 + h 4 ) for the numerical solution of 1D wave equations in polar coordinates, where k > 0 and h > 0 are grid sizes in time and space coordinates, respectively. The proposed method is applicable to problems with singularity. Stability theory of the proposed method is discussed, and numerical examples are given in support of the theoretical results.