Trigonometric Interpolation Based Approach for Second Order ODE with Mixed Boundary Conditions
Numerical Analysis
2025-05-13 v1 Numerical Analysis
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 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.
Cite
@article{arxiv.2505.07183,
title = {Trigonometric Interpolation Based Approach for Second Order ODE with Mixed Boundary Conditions},
author = {Xiaorong Zou},
journal= {arXiv preprint arXiv:2505.07183},
year = {2025}
}