Numerical Solution of Fuzzy Differential Equations by Seventh Order Runge-Kutta Method

2019 ◽  
Vol 10 (7) ◽  
pp. 1518-1528
Author(s):  
P. Rajkumar ◽  
S. Rubanraj
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Seventh Order ◽  
Runge Kutta

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

2020 ◽  
Vol 17 (1) ◽  
pp. 0166
Author(s):  
Hussain Et al.
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Results ◽  
New Method ◽  
Kutta Method ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

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.

scholarly journals Numerical Solution of Fuzzy Delay Differential Equations by Fifth Order Runge-Kutta Method

2021 ◽  
Vol 23 (11) ◽  
pp. 99-109
Author(s):  
T. Muthukumar ◽  
◽  
T. Jayakumar ◽  
D.Prasantha Bharathi ◽  
◽  
...  
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Kutta Method ◽  
Numerical Examples ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Delay Differential ◽  
Fifth Order

In this paper, we develop the numerical solutions of certain type called Fuzzy Delay Differential Equations(FDE) by using fifth order Runge-Kutta method for fuzzy differential equations. This method based on the seikkala derivative and finally we discuss the numerical examples to illustrate the theory.

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

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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