ODE Solvers for Computing Matrix Functions

Abstract

This study investigates the use of ordinary differential equation solvers to estimate the action of matrix functions on vectors. In addition, an evaluation is conducted to ascertain the degree of computational efficiency that is achieved by executing matrix factorisation prior to the implementation of ODE solvers. Three models are employed to analyse the computation of matrix functions acting on vectors, including fractional matrix powers, the matrix exponential, and matrix cosine functions. The performance of the improved Euler, Taylor, Runge–Kutta and Adams–Bashforth methods are compared within these models.