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arXiv · 2505.07183

Trigonometric Interpolation Based Approach for Second Order ODE with Mixed Boundary Conditions

Xiaorong Zou
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Abstract

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.

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Xiaorong Zou. 2025-05-12. Trigonometric Interpolation Based Approach for Second Order ODE with Mixed Boundary Conditions. https://arxiv.org/abs/2505.07183

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