Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation
Hyperbolic partial differential equations are frequently referenced in modeling real-world problems in mathematics and engineering. Therefore, in this study, an initial-boundary value issue is proposed for the pseudo-hyperbolic telegraph equation. By operator method, converting the PDE to an ODE pro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Mahmut Akyigit
2022-12-01
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| Series: | Journal of Mathematical Sciences and Modelling |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/2492275 |
| _version_ | 1797352508656451584 |
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| author | Fatih Özbağ Mahmut Modanlı |
| author_facet | Fatih Özbağ Mahmut Modanlı |
| author_sort | Fatih Özbağ |
| collection | DOAJ |
| description | Hyperbolic partial differential equations are frequently referenced in modeling real-world problems in mathematics and engineering. Therefore, in this study, an initial-boundary value issue is proposed for the pseudo-hyperbolic telegraph equation. By operator method, converting the PDE to an ODE provides an exact answer to this problem. After that, the finite difference method is applied to construct first-order finite difference schemes to calculate approximate numerical solutions. The stability estimations of finite difference schemes are shown, as well as some numerical tests to check the correctness in comparison to the precise solution. The numerical solution is subjected to error analysis. As a result of the error analysis, the maximum norm errors tend to decrease as we increase the grid points. It can be drawn that the established scheme is accurate and effective |
| first_indexed | 2024-03-08T13:16:34Z |
| format | Article |
| id | doaj.art-a8db501178f94a5fbc25447cd11d3988 |
| institution | Directory Open Access Journal |
| issn | 2636-8692 |
| language | English |
| last_indexed | 2024-03-08T13:16:34Z |
| publishDate | 2022-12-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj.art-a8db501178f94a5fbc25447cd11d39882024-01-18T06:19:10ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922022-12-015392981408Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph EquationFatih Özbağ0Mahmut Modanlı1HARRAN ÜNİVERSİTESİHARRAN ÜNİVERSİTESİHyperbolic partial differential equations are frequently referenced in modeling real-world problems in mathematics and engineering. Therefore, in this study, an initial-boundary value issue is proposed for the pseudo-hyperbolic telegraph equation. By operator method, converting the PDE to an ODE provides an exact answer to this problem. After that, the finite difference method is applied to construct first-order finite difference schemes to calculate approximate numerical solutions. The stability estimations of finite difference schemes are shown, as well as some numerical tests to check the correctness in comparison to the precise solution. The numerical solution is subjected to error analysis. As a result of the error analysis, the maximum norm errors tend to decrease as we increase the grid points. It can be drawn that the established scheme is accurate and effectivehttps://dergipark.org.tr/tr/download/article-file/2492275finite difference schemetelegraph equationpseudo-hyperbolic equationstability |
| spellingShingle | Fatih Özbağ Mahmut Modanlı Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation Journal of Mathematical Sciences and Modelling finite difference scheme telegraph equation pseudo-hyperbolic equation stability |
| title | Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation |
| title_full | Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation |
| title_fullStr | Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation |
| title_full_unstemmed | Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation |
| title_short | Stability of Finite Difference Schemes to Pseudo-Hyperbolic Telegraph Equation |
| title_sort | stability of finite difference schemes to pseudo hyperbolic telegraph equation |
| topic | finite difference scheme telegraph equation pseudo-hyperbolic equation stability |
| url | https://dergipark.org.tr/tr/download/article-file/2492275 |
| work_keys_str_mv | AT fatihozbag stabilityoffinitedifferenceschemestopseudohyperbolictelegraphequation AT mahmutmodanlı stabilityoffinitedifferenceschemestopseudohyperbolictelegraphequation |