Table of Contents
ISRN Computational Mathematics
Volume 2013 (2013), Article ID 710529, 8 pages
http://dx.doi.org/10.1155/2013/710529
Research Article

Applying Cubic B-Spline Quasi-Interpolation to Solve 1D Wave Equations in Polar Coordinates

Department of Applied Mathematics, School of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht 41938, Iran

Received 27 August 2013; Accepted 14 October 2013

Academic Editors: Y. Peng and J. G. Zhou

Copyright © 2013 Hossein Aminikhah and Javad Alavi. 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 provide numerical solution to the one-dimensional wave equations in polar coordinates, based on the cubic B-spline quasi-interpolation. The numerical scheme is obtained by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a forward difference to approximate the time derivative of the dependent variable. The accuracy of the proposed method is demonstrated by three test problems. The results of numerical experiments are compared with analytical solutions by calculating errors -norm and -norm. The numerical results are found to be in good agreement with the exact solutions. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement.