scholarly journals Fourth-Order Improved Runge–Kutta Method for Directly Solving Special Third-Order Ordinary Differential Equations

2017 ◽  
Vol 41 (2) ◽  
pp. 429-437 ◽  
Author(s):  
Kasim Abbas Hussain ◽  
Fudziah Ismail ◽  
Norazak Senu ◽  
Faranak Rabiei
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Kutta Method ◽  
Third Order ◽  
Runge Kutta Method ◽  
Runge Kutta

scholarly journals Study of Numerical Solution of Fourth Order Ordinary Differential Equations by fifth order Runge-Kutta Method

2019 ◽  
pp. 230-238
Author(s):  
Najmuddin Ahamad ◽  
Shiv Charan
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fourth Order ◽  
Initial Value Problems ◽  
Computational Cost ◽  
Kutta Method ◽  
Initial Value ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper we present fifth order Runge-Kutta method (RK5) for solving initial value problems of fourth order ordinary differential equations. In this study RK5 method is quite efficient and practically well suited for solving boundary value problems. All mathematical calculation performed by MATLAB software for better accuracy and result. The result obtained, from numerical examples, shows that this method more efficient and accurate. These methods are preferable to some existing methods because of their simplicity, accuracy and less computational cost involved.

scholarly journals Fuzzy version of a developed fourth order Runge Kutta method for solving differential equations with fuzzy initial values

2016 ◽  
Author(s):  
Amirah Ramli ◽  
Rokiah @ Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Abdul Razak Salleh
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Kutta Method ◽  
Initial Values ◽  
Runge Kutta Method ◽  
Runge Kutta

scholarly journals DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1998 ◽  
Vol 3 (1) ◽  
pp. 45-56
Author(s):  
T. Cîrulis ◽  
O. Lietuvietis
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Matrix Method ◽  
Iteration Procedure ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Systems Of Differential Equations ◽  
Runge Kutta ◽  
Degenerate Matrix

Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given.

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