The Differential Transform Method (DTM): Solution of Differential Equations
Recent Studies in Mathematics and Computer Science Vol. 2,
Page 87-99
Abstract
In this chapter, linear and nonlinear differential equations are solved. The calculations are carried out by using differential transformation method (DTM) which is a semi-numerical–analytical solution technique. By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related initial conditions are transformed into a set of algebraic equations. The properties of differential transformation is briefly introduced, and then applied for the number of problems. The current results are then compared with those derived from the classical Runge-Kutta method (RK4) order to verify the accuracy of the proposed method. The findings disclose that the DTM can achieve more suitable results in predicting the solution of such problems.
Keywords:
- Riccati equation
- duffing equation
- integro-differential equations
- chaotic solution
- differential transforms method
- Runge-Kutta 4 (RK4) method
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