## A NEW MODIFICATION OF THE DIFFERENTIAL TRANSFORM METHOD

Published: 2020-10-07

Page: 38-51

HELENA NAYAR *

School of Mathematics and Natural Sciences, The Copperbelt University, Kitwe, Zambia

PATRICK AZERE PHIRI

School of Mathematics and Natural Sciences, The Copperbelt University, Kitwe, Zambia

*Author to whom correspondence should be addressed.

### Abstract

In this article, a new modification of the Differential Transform Method, named the ModDTM, is being introduced as a method suitable for solving (1 + 1) partial differential equations, with initial conditions that are specified at the initial value of the spatial variable. Definitions and properties of the method are developed and then applied for solving two nonlinear partial differential equations, namely, the Rosenau-Hyman equation and the Newell-Whitehead-Segel equation, to examine the effectiveness of the method. The solutions obtained are compared with the exact solutions and the solutions by the Reduced Differential Transform Method. It is assessed that the ModDTM is an effective method for solving (1+1) partial differential equations when the attached initial conditions pertain to the spatial variable.

Keywords: ModDTM, differential transform method, reduced differential transform method, Rosenau-Hyman equation, Newell-Whitehead-Segel equation.

#### How to Cite

NAYAR, H., & PHIRI, P. A. (2020). A NEW MODIFICATION OF THE DIFFERENTIAL TRANSFORM METHOD. Asian Journal of Mathematics and Computer Research, 27(3), 38–51. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/5475

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