Table of Contents
ISRN Computational Mathematics
Volume 2012 (2012), Article ID 302923, 6 pages
http://dx.doi.org/10.5402/2012/302923
Research Article

Cubic Spline Method for 1D Wave Equation in Polar Coordinates

1Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India
2Department of Mathematics, Deenbandhu Chhotu Ram University of Science & Technology, Murthal 131039, India

Received 10 September 2011; Accepted 28 September 2011

Academic Editors: P. B. Vasconcelos and J. G. Zhou

Copyright © 2012 R. K. Mohanty et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using nonpolynomial cubic spline approximation in space and finite difference in time direction, we discuss three-level implicit difference scheme of 𝑂(π‘˜2+β„Ž4) for the numerical solution of 1D wave equations in polar coordinates, where π‘˜>0 and β„Ž>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.