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Solvable systems of linear differential equations

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Abstract

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Prince Edward Island Charlottetown, Prince Edward Island, C1A 4P3, Canada

    Katherine M. Robertson & Nasser Saad

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  1. Katherine M. Robertson
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  2. Nasser Saad
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Correspondence to Nasser Saad.

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Robertson, K.M., Saad, N. Solvable systems of linear differential equations. J. Appl. Math. Comput. 31, 475–494 (2009). https://doi.org/10.1007/s12190-008-0225-2

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  • DOI: https://doi.org/10.1007/s12190-008-0225-2

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