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The Fornberg-Whitham Equation Solved by the Differential Transform Method

2020; Linguagem: Inglês

10.9734/jamcs/2020/v35i730306

2456-9968

Helena Nayar, Patrick Azere Phiri,

Fractional Differential Equations Solutions

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.