Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 210261, 14 pages
Research Article

Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation

Department of Elementary Mathematics Education, Mevlana University, 42003 Konya, Turkey

Received 3 September 2011; Accepted 31 October 2011

Academic Editor: Hassan A. El-Morshedy

Copyright © 2011 Mehmet Emir Koksal. 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.


The second-order one-dimensional linear hyperbolic equation with time and space variable coefficients and nonlocal boundary conditions is solved by using stable operator-difference schemes. Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. These schemes are shown to be absolutely stable, and the numerical results are presented to compare the accuracy and the execution times. It is naturally seen that the second-order difference schemes are much more advantages than the first-order ones. Although one of the second-order difference scheme is less preferable than the other one according to CPU (central processing unit) time consideration, it has superiority when the accuracy weighs more importance.