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

• Main Authors: Vijeyata Chauhan, Pankaj Kumar Srivastava
• Format: Article
• Language: English
• Published: International Journal of Mathematical, Engineering and Management Sciences 2019-04-01
• Series: International Journal of Mathematical, Engineering and Management Sciences
• Subjects: Runge-Kutta algorithm; Convergence of method; Implicit-Explicit method; Ordinary and partial differential equations
• Online Access: https://www.ijmems.in/assets//30-ijmems-18-272_vol.-4%2c-no.-2%2c-375%E2%80%93386%2c-2019.pdf

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.