Solutions of Initial Value Problems Using Fifth-Order Runge-Kutta Method Using Excel Spreadsheet

2001 ◽  
Vol 2 (1) ◽  
pp. 44-47 ◽  
Author(s):  
Fae`q A.A. Radwan .
Keyword(s):  
Initial Value Problems ◽  
Kutta Method ◽  
Initial Value ◽  
Excel Spreadsheet ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

scholarly journals Accurate Numerical Method for Singular Initial-Value Problems

2021 ◽  
Vol 08 (03) ◽  
pp. 01-11
Author(s):  
Tesfaye Aga Bullo ◽  
Gemechis File Duressa ◽  
Gashu Gadisa Kiltu
Keyword(s):  
Numerical Method ◽  
Initial Value Problems ◽  
Approximate Solutions ◽  
Stability And Convergence ◽  
Order System ◽  
Kutta Method ◽  
Initial Value ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Fifth Order

In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.

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 Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPS

2021 ◽  
Vol 50 (6) ◽  
pp. 1799-1814
Author(s):  
Norazak Senu ◽  
Nur Amirah Ahmad ◽  
Zarina Bibi Ibrahim ◽  
Mohamed Othman
Keyword(s):  
Fourth Order ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Numerical Study ◽  
Kutta Method ◽  
Initial Value ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
The Stability

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

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