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The homotopy analysis Rangaig transform method for nonlinear partial differential equations

Ziane Djelloul, Cherif Mountassir Hamdi

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 2

111--122

The idea suggested in this article is to combine the Rangaig transform with the homotopy analysis method in order to facilitate the solution of nonlinear partial differentia equations. This method may be called the homotopy analysis Rangaig transform method (HARTM). The proposed example results showed that HARTM is an effective method for solving nonlinear partial differential equations.

Generalized solutions to a characteristic Cauchy problem

Allaud E, Devoue V

Journal of Applied Analysis

2013

Vol. 19, nr 1

1--29

We give a meaning to the nonlinear characteristic Cauchy problem for the wave equation in base form by replacing it by a family of non-characteristic ones. This leads to a well-formulated problem in an appropriate algebra of generalized functions. We prove existence of a solution and we precise how it depends on the choice made. We also check that in the classical case (non-characteristic) our new solution coincides with the classical one.

Application of Waterloo MAPLE 9.5 and Wolfram MATHEMATICA 5.1 software for analytic solving of certain nonlinear partial differential equations of physics

Stępień Ł.T.

Computer Science

2008

Vol. 9

147-155

In the current paper some applications of the packet MAPLE (v. 9.5) for analytic solying of certain nonline partial differential eguations have been presented. Additionally, for graphic presentation of the found solutions packet MATHEMATICA (v. 5.1) has been applied.

W niniejszej pracy zostały przedstawione zastosowania pakietu MAPLE (wersja 9.5 do analitycznego znajdywania rozwiązań wybranych nieliniowych równań różniczkowych cząstkowych. Do prezentacji graficznej tych rozwiązań użyto pakietu MATHEMATICA (wersje 5.1).