Convergence of Differential Transform Method for Ordinary Differential Equations
Journal of Advances in Mathematics and Computer Science · pp. 1–17 · Published 10 Oct 2017
10.9734/JAMCS/2017/36489Abstract
Differential transform method (DTM) as a method for approximating solutions to differential equations have many theorems that are often used without recourse to their proofs. In this paper, attempts are made to compile these proofs. This paper also proceeds to establish the convergence of the DTM for ordinary differential equations. This paper establishes that if the solution of an ordinary differential equation can be written as Taylors' expansion, then the solution can be obtained using the DTM. This is also demonstrated with some numerical examples.
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