Collocation Method by Exponential Functions for Solving the System of Differential Equations and Error Bound

Abstract

This paper introduces three novel numerical approaches for solving linear matrix differential equations. Leveraging exponential functions and collocation points, these methods transform the original problem into a system of algebraic equations through matrix operations. The first method employs negative exponential functions, the second adopts positive exponential functions, and the third combines both into extended exponential functions. Error analysis is provided, and an error problem formulated via the residual function is solved using the proposed techniques to estimate errors. Numerical examples demonstrate the effectiveness of the methods and the accuracy of the error estimation.