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International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749


Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations

Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations

Vijeyata Chauhan
Department of Mathematics, Jaypee Institute of Information Technology, Noida, India.

Pankaj Kumar Srivastava
Department of Mathematics, Jaypee Institute of Information Technology, Noida, India.

DOI https://dx.doi.org/10.33889/IJMEMS.2019.4.2-030

Received on September 25, 2018
  ;
Accepted on December 26, 2018

Abstract

The Runge-Kutta method is a one step method with multiple stages, the number of stages determine order of method. The method can be applied to work out on differential equation of the type’s explicit, implicit, partial and delay differential equation etc. The present paper describes a review on recent computational techniques for solving differential equations using Runge-Kutta algorithm of various order. This survey includes the summary of the articles of last decade till recent years based on third; fourth; fifth and sixth order Runge-Kutta methods. Along with this a combination of these methods and various other type of Runge-Kutta algorithm based articles are included. Comparisons of methods with own critical comments as remarks have been included.

Keywords- Runge-Kutta algorithm, Convergence of method, Implicit-Explicit method, Ordinary and partial differential equations.

Citation

Chauhan, V., & Srivastava, P. K. (2019). Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations. International Journal of Mathematical, Engineering and Management Sciences, 4(2), 375-386. https://dx.doi.org/10.33889/IJMEMS.2019.4.2-030.

Conflict of Interest

Both authors have contributed equally in this work. The authors declare that there is no conflict of interest for this publication.

Acknowledgements

The authors extend their appreciation to the anonymous reviewers for their valuable suggestions.

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