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