Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/210261 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552259718742016 |
|---|---|
| author | Mehmet Emir Koksal |
| author_facet | Mehmet Emir Koksal |
| author_sort | Mehmet Emir Koksal |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-cf5d3d1669f9459ea60bcd00e42da26c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-cf5d3d1669f9459ea60bcd00e42da26c2025-02-03T05:59:10ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2011-01-01201110.1155/2011/210261210261Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave EquationMehmet Emir Koksal0Department of Elementary Mathematics Education, Mevlana University, 42003 Konya, TurkeyThe 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.http://dx.doi.org/10.1155/2011/210261 |
| spellingShingle | Mehmet Emir Koksal Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation Discrete Dynamics in Nature and Society |
| title | Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation |
| title_full | Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation |
| title_fullStr | Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation |
| title_full_unstemmed | Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation |
| title_short | Recent Developments on Operator-Difference Schemes for Solving Nonlocal BVPs for the Wave Equation |
| title_sort | recent developments on operator difference schemes for solving nonlocal bvps for the wave equation |
| url | http://dx.doi.org/10.1155/2011/210261 |
| work_keys_str_mv | AT mehmetemirkoksal recentdevelopmentsonoperatordifferenceschemesforsolvingnonlocalbvpsforthewaveequation |