Open AccessThe Fornberg-Whitham Equation Solved by the Differential Transform Method
Author(s) -
Heleyar,
Patrick Azere Phiri
Publication year - 2020
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2020/v35i730306
Subject(s) - first order partial differential equation , mathematics , partial differential equation , separable partial differential equation , method of characteristics , mathematical analysis , differential equation , nonlinear system , hyperbolic partial differential equation , variable (mathematics) , numerical partial differential equations , differential algebraic equation , ordinary differential equation , physics , quantum mechanics
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.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom