Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay

Abstract

In this work, we successfully extended two-dimensional differential transform method and their reduced form, by presenting and proving some theorems, to obtain the solution of partial differential equations (PDEs) with proportional delay in t and shrinking in x. Theorems are presented in the most general form to cover a wide range of PDEs, being linear or nonlinear and constant or variable coefficient. In order to show the power and robustness of the present methods and to illustrate the pertinent features of related theorems, some examples are presented.

Keywords:

• proportional delay PDEs
• delay equations
• differential transformation method
• reduced differential transformation method
• nonlinear PDEs
• closed-form solution

2000 AMS Subject Classifications :

• 60Hxx
• 34Kxx

Acknowledgements

The authors wish to express their gratitude to an anonymous referees whose comments and suggestions proved most constructive, informative, and useful during the revision of this manuscript. Due to their valuable comments and suggestions, the first version of the paper was considerably revised. Also, the first author (Reza Abazari) would like to thank the Islamic Azad University, Young Researchers Club, Ardabil Branch for its financial support.