Electron. J. Diff. Eqns., Vol. 2003(2003), No. 79, pp. 1-18.

Analytical solution of linear ordinary differential equations by differential transfer matrix method

Sina Khorasani & Ali Adibi

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.

Submitted June 2, 2003. Published August 5, 2003.
Math Subject Classifications: 34A05, 34A25, 34A30.
Key Words: Ordinary differential equations, differential transfer matrix method, matrix exponential.

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Sina Khorasani
School of Electrical and Computer Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0250, USA
email: sina.khorasani@ece.gatech.edu
Ali Adibi
School of Electrical and Computer Engineering
Georgia Institute of Technology
Atlanta, GA 30332-0250, USA

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