Solution of Modified Equations of Emden-type by Differential Transform Method: New Perspectives | Chapter 9 | Recent Studies in Mathematics and Computer Science Vol. 2

In this paper the Modified Equations of Emden type (MEE), ̈ + ̇ + =0 is solved numerically by the differential transform method. This technique doesn’t require any discretization, linearization or small perturbations and therefore it reduces significantly the numerical computation. The current results of this paper are in excellent agreement with those provided by Chandrasekar et al. [1] and thereby illustrate the reliability and the performance of the differential transform method. We have also compared the results with the classical Runge-Kutta 4 (RK4) Method.

Author(s) Details

Dr. Supriya Mukherjee
 Department of Mathematics, Gurudas College, 1/1 Suren Sarkar Road, Narkeldanga, Kolkata - 700054, West Bengal, India.

Dr. Banamali Roy
Department of Mathematics, Bangabasi Evening College, 19, Rajkumar Chakraborty Sarani, Kolkata - 700009, West Bengal, India.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/182

The Differential Transform Method (DTM): Solution of Differential Equations | Chapter 8 | Recent Studies in Mathematics and Computer Science Vol. 2

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.

Author (s) Details

Dr. Supriya Mukherjee
Department of Mathematics, Gurudas College, 1/1 Suren Sarkar Road, Narkeldanga, Kolkata - 700054, West Bengal, India.

Dr. Banamali Roy
Department of Mathematics, Bangabasi Evening College, 19, Rajkumar Chakraborty Sarani, Kolkata - 700009, West Bengal, India.

View Book :- http://bp.bookpi.org/index.php/bpi/catalog/book/182