A novel numerical method on the resolution of the time-invariant systems response

Abstract

An algorithm for evaluation of time response to a time-invariant system based on Haar wavelets is proposed. The system is assumed to be governed by a high order linear differential equation with constant coefficients. The main objective of this study is to convert a differential equation into an algebraic-form equation and provide an elegant approach for computer programming. By the method, the computation complexity can be greatly reduced or much simplified in calculate the time response of a time-invariant system. The accurate and fastness of the method have been demonstrated by the examples of integration of the stiff systems.