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

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dc.creatorKhorasani, Sina
dc.creatorAdibi, Ali
dc.date2003-01-09
dc.date2003-03-12
dc.date.accessioned2026-07-07T04:29:43Z
dc.date.available2026-07-07T04:29:43Z
dc.descriptionWe report a new analytical method for 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 $n$th-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. We show that the Abel-Liouville-Ostogradski theorem can be easily recovered through this approach.
dc.identifierhttps://arxiv.org/abs/math-ph/0301010
dc.identifierhttp://arxiv.org/abs/math-ph/0301010
dc.identifierElectronic Journal of Differential Equations, Vol. 2003, No. 79, pp. 1-18 (2003)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57260
dc.subjectMathematical Physics
dc.subjectClassical Analysis and ODEs
dc.subject34A05; 34A25; 34A30
dc.titleAnalytical solution of linear ordinary differential equations by differential transfer matrix method
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