An Application of Trigonometric Interpolation on Solving a Non-Linear ODE System with Constraints

In this paper, a trigonometric interpolation-based method is used to solve general non-linear ODE systems with certain constraints due to conservation laws in physics, biology, and engineering. In the case that a target solution of ODE is highly oscillated or rapid changed somewhere in its domain, the algorithm is expected to outperform significantly difference-based methods such as Runge-Kutta rules, which has been confirmed by several numerical experiments conducted in this paper.