Analytical solution of linear ordinary differential equations by differential transfer matrix method
Date
2003-08-05
Authors
Khorasani, Sina
Adibi, Ali
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We report a new analytical method for finding the exact solution of homogeneous linear ordinary differential equations with arbitrary order and variable coefficients. The method is based on the definition of jump transfer matrices and their extension into limiting differential form. The approach reduces the nth-order differential equation to a system of n linear differential equations with unity order. The full analytical solution is then found by the perturbation technique. The important feature of the presented method is that it deals with the evolution of independent solutions, rather than its derivatives. We prove the validity of method by direct substitution of the solution in the original differential equation. We discuss the general properties of differential transfer matrices and present several analytical examples, showing the applicability of the method.
Description
Keywords
Ordinary differential equations, Differential transfer matrix method, Matrix exponential
Citation
Khorasani, S., & Adibi, A. (2003). Analytical solution of linear ordinary differential equations by differential transfer matrix method. <i>Electronic Journal of Differential Equations, 2003</i>(79), pp. 1-18.
Rights
Attribution 4.0 International