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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


7th -Order Caudrey-Dodd-Gibbon Equation and Fisher-Type Equation by Homotopy Analysis Method

7th -Order Caudrey-Dodd-Gibbon Equation and Fisher-Type Equation by Homotopy Analysis Method

Ankita Sharma
Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Saharanpur Campus, Saharanpur, India.

Rajan Arora
Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Saharanpur Campus, Saharanpur, India.

DOI https://doi.org/10.33889/IJMEMS.2020.5.2.022

Received on June 27, 2019
  ;
Accepted on December 16, 2019

Abstract

In this paper, we first describe the methodology of the Homotopy Analysis Method (HAM) which is an analytical technique and then employ it to some of the non-linear problems which are used in different fields of sciences like plasma physics, fluid dynamics, laser optics, biology, chemical kinetics, nucleation kinetics, physiology, etc. Approximate series solutions have been obtained and the results are compared with the closed form solutions of the equations, which show that this technique gives high accurate results. HAM is a reliable technique, easy to use and is widely applicable to a large class of non-linear differential equations. MATHEMATICA software package has been used for computations.

Keywords- Homotopy analysis method, 7th -order Caudrey-Dodd-Gibbon equation, Fisher-type equation.

Citation

Sharma, A., & Arora, R. (2020). 7th -Order Caudrey-Dodd-Gibbon Equation and Fisher-Type Equation by Homotopy Analysis Method. International Journal of Mathematical, Engineering and Management Sciences, 5(2), 272-282. https://doi.org/10.33889/IJMEMS.2020.5.2.022.

Conflict of Interest

The authors confirm no conflict of interests.

Acknowledgements

The efforts made by the respected editor and reviewers of IJMEMS are highly appreciated for helping in enhancing the quality of the paper.

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