The Fornberg-Whitham Equation Solved by the Differential Transform Method
Helena Nayar *
Department of Mathematics, School of Mathematics and Natural Sciences, The Copperbelt University, Kitwe, Zambia
Patrick Azere Phiri
Department of Mathematics, School of Mathematics and Natural Sciences, The Copperbelt University, Kitwe, Zambia.
*Author to whom correspondence should be addressed.
Abstract
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 of
the 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.
Keywords: Differential Transform method, Fornberg-Whitham equation.