Abstract
In this paper Pade Embedded Differential Transformation is proposed for the solution of higher order nonlinear or linear Ordinary Differential Equations (ODE’s). The proposed approach provides a better iterative procedure to find the spectrum of the analytic solutions compared to the classical differential transformation. Illustrative examples are presented to show the preciseness and effectiveness of the proposed method.
Highlights
In the 1980’s, Zhou [1] proposed the Differential Transformation (DT) Method for the solution of electrical circuits and, many researchers have applied this method for solving different types of differential equations [1]
It is important to note that a large amount of research works has been devoted to the application of DT method to a wide class of stochastic and deterministic problems involving differential, integro-differential and systems of such equations [6,7,8,9,10,13]
The differential transformation technique is based upon Taylor series expansion and provides iterative procedures to obtain higher-order power series
Summary
In the 1980’s, Zhou [1] proposed the Differential Transformation (DT) Method for the solution of electrical circuits and, many researchers have applied this method for solving different types of differential equations [1]. It is important to note that a large amount of research works has been devoted to the application of DT method to a wide class of stochastic and deterministic problems involving differential, integro-differential and systems of such equations [6,7,8,9,10,13]. Chen applied DT method to handle nonlinear heat conduction problems [6] and used this method to solve the transient advective dispersive transport equation[11]. After transforming the differential equation in to the K domain, the solution can be obtained by finite-term Taylor series plus a remainder as where
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