scholarly journals A NEW FIFTH-ORDER WEIGHTED RUNGE-KUTTA ALGORITHM BASED ON HERONIAN MEAN FOR INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS

2017 ◽  
Vol 35 (1_2) ◽  
pp. 191-204
Author(s):  
M. CHANDRU ◽  
R. PONALAGUSAMY ◽  
P.J.A. ALPHONSE
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Initial Value ◽  
Runge Kutta ◽  
Fifth Order ◽  
Heronian Mean

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.

A RUNGE–KUTTA–FEHLBERG CODE FOR THE COMPLEX PLANE: COMPARING WITH SIMILAR CODES BY APPLYING TO POLYTROPIC MODELS

2012 ◽  
Vol 23 (05) ◽  
pp. 1250038 ◽  
Author(s):  
V. S. GEROYANNIS ◽  
F. N. VALVI
Keyword(s):  
Differential Equations ◽  
Neutron Stars ◽  
Complex Variable ◽  
Initial Value Problems ◽  
High Complexity ◽  
Initial Value ◽  
General Relativistic ◽  
Runge Kutta ◽  
Fifth Order ◽  
Complex Valued

In this paper, we modify the Runge–Kutta–Fehlberg code of fourth and fifth order with the purpose of solving initial value problems established on ordinary differential equations involving complex-valued functions of one complex variable, which are allowed to have high complexity in their definition, when integration along prescribed complex paths is required. Such initial value problems arise in certain astrophysical issues, like the polytropic models, applied to polytropic stars, and the general-relativistic polytropic models, applied to neutron stars. Comparison with similar codes is made by applying to these models.

scholarly journals Optimization of one-step hybrid method for direct solution of fifth order ordinary differential equations of initial value problems

2021 ◽  
Vol 9 (1) ◽  
pp. 239-249
Author(s):  
Roseline Bosede Ogunrinde ◽  
Ololade Funmilayo Fayose ◽  
Taiwo Stephen Fayose
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Hybrid Method ◽  
Basis Function ◽  
Initial Value Problems ◽  
Test Problems ◽  
Direct Solution ◽  
Initial Value ◽  
Unknown Parameters ◽  
Fifth Order

This paper focuses on the derivation, analysis and implementation of a hybrid method by optimizing the order of the method by introduction of six-hybrid points for direct solution of fifth order ordinary differential equations of initial value problems (IVPs). Power series was used as the basis function for the solution of the IVP. The basis function was interpolated at some selected hybrid points whereas the fifth derivative of the approximate solution was collocated at all the interval of integration of the method to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was tested with two linear test problems to confirm its accuracy and usability. The comparison of the results with some existing methods shows the superiority of the accuracy of the method.

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