scholarly journals A Numerical Computation of a System of Linear and Nonlinear Time Dependent Partial Differential Equations Using Reduced Differential Transform Method

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Brajesh Kumar Singh ◽  
Mahendra
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Transform Method ◽  
Time Dependent ◽  
Test Problems ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Linear And Nonlinear ◽  
Reduced Differential Transform Method

This paper deals with an analytical solution of an initial value system of time dependent linear and nonlinear partial differential equations by implementing reduced differential transform (RDT) method. The effectiveness and the convergence of RDT method are tested by means of five test problems, which indicates the validity and great potential of the reduced differential transform method for solving system of partial differential equations.

scholarly journals The Fornberg-Whitham Equation Solved by the Differential Transform Method

2020 ◽  
pp. 85-95
Author(s):  
Helena Nayar ◽  
Patrick Azere Phiri
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Differential Transform Method ◽  
Time Dependent ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform ◽  
Whitham Equation ◽  
Temporal Variable

The Differential Transform Method is a powerful analytical method that can solve nonlinear partial differential equations. Yet, the method cannot be used to solve time-dependent partial differential equations that involve more than one partial derivative with respect to the temporal variable t when they are of the same order, as in the case of the Fornberg-Whitham type equations. In this paper, a new theorem is devised to overcome the aforementioned problem ofthe method, and it has been successfully applied to solve the Fornberg-Whitham equation. The other equations belonging to this group of equations, such as the Camassa-Holm equation and the Degasperi-Procesi equation, may also be solved by this approach.

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