Trigonometric Interpolation Based Approach for Second Order ODE with Mixed Boundary Conditions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915283238649856 |
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| author | Zou, Xiaorong |
| author_facet | Zou, Xiaorong |
| contents | This paper proposes a trigonometric interpolation-based approach (TIBA) to approximate solutions of mixed boundary value problems of second-order ODEs. TIBA leverages the analytic attractiveness of a trigonometric polynomial to reformulate the dynamics of $y, y',y''$ implied by ODE and boundary conditions. TIBA is particularly attractive for a linear ODE where the solution can be obtained directly by solving a linear system. The framework can be used to solve integro-differential equations. Numerical tests have been conducted to assess TIBA's performance regarding convergence, existence, and uniqueness of solution under various boundary conditions with expected results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trigonometric Interpolation Based Approach for Second Order ODE with Mixed Boundary Conditions Zou, Xiaorong Numerical Analysis Primary 65T40, Secondary 65T50 This paper proposes a trigonometric interpolation-based approach (TIBA) to approximate solutions of mixed boundary value problems of second-order ODEs. TIBA leverages the analytic attractiveness of a trigonometric polynomial to reformulate the dynamics of $y, y',y''$ implied by ODE and boundary conditions. TIBA is particularly attractive for a linear ODE where the solution can be obtained directly by solving a linear system. The framework can be used to solve integro-differential equations. Numerical tests have been conducted to assess TIBA's performance regarding convergence, existence, and uniqueness of solution under various boundary conditions with expected results. |
| title | Trigonometric Interpolation Based Approach for Second Order ODE with Mixed Boundary Conditions |
| topic | Numerical Analysis Primary 65T40, Secondary 65T50 |
| url | https://arxiv.org/abs/2505.07183 |