The Differential Transform Method (DTM): Solution of Differential Equations

Supriya Mukherjee; Banamali Roy

Supriya Mukherjee Department of Mathematics, Gurudas College, 1/1 Suren Sarkar Road, Narkeldanga, Kolkata - 700054, West Bengal, India.
Banamali Roy Department of Mathematics, Bangabasi Evening College, 19, Rajkumar Chakraborty Sarani, Kolkata - 700009, West Bengal, India.

Keywords: Riccati equation, duffing equation, integro-differential equations, chaotic solution, differential transforms method, Runge-Kutta 4 (RK4) method

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-numericalanalytical 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.