A New Two Derivative FSAL Runge-Kutta Method of Order Five in Four Stages

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

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The Runge-Kutta method with fixed and variable parameters for solution of systems of first-order ordinary differential equations

Applications of Mathematics ◽

10.21136/am.1975.103582 ◽

1975 ◽

Vol 20 (3) ◽

pp. 166-185

Author(s):

Siegfried Scholz

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Kutta Method ◽

Variable Parameters ◽

First Order ◽

Runge Kutta Method ◽

Runge Kutta

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A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations

10.1063/1.4801239 ◽

2013 ◽

Author(s):

Yusuf Dauda Jikantoro ◽

Fudziah Ismail ◽

Noraz Senu

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Fourth Order ◽

Kutta Method ◽

First Order ◽

Runge Kutta Method ◽

Runge Kutta

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A highly efficient implicit Runge-Kutta method for first order ordinary differential equations

African Journal of Mathematics and Computer Science Research ◽

10.5897/ajmcsr2014.0551 ◽

2014 ◽

Vol 7 (5) ◽

pp. 55-60 ◽

Cited By ~ 1

Author(s):

A. Agam S. ◽

A. Yahaya Y.

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Kutta Method ◽

First Order ◽

Highly Efficient ◽

Runge Kutta Method ◽

Runge Kutta

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A Numerical Solution of First order Simultaneous Fuzzy Differential Equations by Sixth Order Runge-Kutta Method

International Journal for Research in Applied Science and Engineering Technology ◽

10.22214/ijraset.2019.3477 ◽

2019 ◽

Vol 7 (3) ◽

pp. 2606-2615

Author(s):

P. Rajkumar

Keyword(s):

Differential Equations ◽

Numerical Solution ◽

Sixth Order ◽

Kutta Method ◽

First Order ◽

Runge Kutta Method ◽

Runge Kutta

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Numerical Solution of Volterra Integro-Differential Equations Using Improved Runge-Kutta Methods

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.892.193 ◽

2019 ◽

Vol 892 ◽

pp. 193-199

Author(s):

Faranak Rabiei ◽

Fatin Abd Hamid ◽

Nafsiah Md Lazim ◽

Fudziah Ismail ◽

Zanariah Abdul Majid

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Numerical Solution ◽

Quadrature Rule ◽

Numerical Results ◽

Test Problems ◽

Kutta Method ◽

Runge Kutta Method ◽

Runge Kutta ◽

Interpolation Polynomials

In this paper, we proposed the numerical solution of Volterra integro-differential equations of the second kind using Improved Runge-Kutta method of order three and four with 2 stages and 4 stages, respectively. The improved Runge-kutta method is considered as two-step numerical method for solving the ordinary differential equation part and the integral operator in Volterra integro-differential equation is approximated using quadrature rule and Lagrange interpolation polynomials. To illustrate the efficiency of proposed methods, the test problems are carried out and the numerical results are compared with existing third and fourth order classical Runge-Kutta method with 3 and 4 stages, respectively. The numerical results showed that the Improved Runge-Kutta method by achieving the higher accuracy performed better results than existing methods.

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