Academic Journal
High-order compact difference methods for solving two-dimensional nonlinear wave equations
| العنوان: | High-order compact difference methods for solving two-dimensional nonlinear wave equations |
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| المؤلفون: | Shuaikang Wang, Yunzhi Jiang, Yongbin Ge |
| المصدر: | Electronic Research Archive, Vol 31, Iss 6, Pp 3145-3168 (2023) |
| بيانات النشر: | AIMS Press, 2023. |
| سنة النشر: | 2023 |
| المجموعة: | LCC:Mathematics LCC:Applied mathematics. Quantitative methods |
| مصطلحات موضوعية: | nonlinear wave equation, nonlinear compact difference scheme, three-level linearized compact difference scheme, coupled sine-gordon equations, Mathematics, QA1-939, Applied mathematics. Quantitative methods, T57-57.97 |
| الوصف: | Nonlinear wave equations are widely used in many areas of science and engineering. This paper proposes two high-order compact (HOC) difference schemes with convergence orders of $ O\left({{\tau ^4} + h_x^4 + h_y^4} \right) $ that can be used to solve nonlinear wave equations. The first scheme is a nonlinear compact difference scheme with three temporal levels. After calculating the second-order spatial derivatives of the previous time level using the Padé scheme, numerical solutions of the next time level are obtained through repeated iterations. The second scheme is a three-level linearized compact difference scheme. Unlike the first scheme, iterations are not required and it obtains numerical solutions through an explicit calculation. The two proposed schemes are applied to solutions of the coupled sine-Gordon equations. Finally, some numerical experiments are presented to confirm the effectiveness and accuracy of the proposed schemes. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 2688-1594 |
| Relation: | https://doaj.org/toc/2688-1594 |
| DOI: | 10.3934/era.2023159?viewType=HTML |
| DOI: | 10.3934/era.2023159 |
| URL الوصول: | https://doaj.org/article/fe10b5a6dad044fb8c9ca8a7886bcad7 |
| رقم الانضمام: | edsdoj.fe10b5a6dad044fb8c9ca8a7886bcad7 |
| قاعدة البيانات: | Directory of Open Access Journals |
| تدمد: | 26881594 |
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| DOI: | 10.3934/era.2023159?viewType=HTML |