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Advances in Numerical Analysis
Volume 2013 (2013), Article ID 470480, 8 pages
http://dx.doi.org/10.1155/2013/470480
Research Article

New Nonpolynomial Spline in Compression Method of for the Solution of 1D Wave Equation in Polar Coordinates

1Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, Delhi 110 007, India
2Department of Applied Mathematics, South Asian University, Akbar Bhawan, Delhi 110021, India

Received 21 December 2012; Revised 6 July 2013; Accepted 25 July 2013

Academic Editor: Rüdiger Weiner

Copyright © 2013 Venu Gopal 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

We propose a three-level implicit nine point compact finite difference formulation of order two in time and four in space direction, based on nonpolynomial spline in compression approximation in -direction and finite difference approximation in -direction for the numerical solution of one-dimensional wave equation in polar coordinates. We describe the mathematical formulation procedure in detail and also discussed the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.