scholarly journals Diagonally implicit Runge-Kutta method of order four with minimum phase-lag for solving first order linear ODEs

2014 ◽  
Author(s):  
Fudziah Ismail ◽  
Mohammed M. Salih
Keyword(s):  
Phase Lag ◽  
Minimum Phase ◽  
Kutta Method ◽  
Order Linear ◽  
First Order ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Order Four ◽  
Linear Odes

scholarly journals Numerical Solution of First Order Linear Differential Equations in Fuzzy Environment by Modified Runge-Kutta- Method and Runga-Kutta-Merson-Method under generalized H-differentiability and its Application in Industry

2017 ◽  
Author(s):  
Sankar Prasad Mondal ◽  
Susmita Roy ◽  
Biswajit Das ◽  
Animesh Mahata
Keyword(s):  
Numerical Solution ◽  
Kutta Method ◽  
Order Linear ◽  
First Order ◽  
Generalized Hukuhara Derivative ◽  
Fuzzy Environment ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Linear Differential ◽  
Fuzzy Solutions

The paper presents an adaptation of numerical solution of first order linear differential equation in fuzzy environment. The numerical method is re-established and studied with fuzzy concept to estimate its uncertain parameters whose values are not precisely known. Demonstrations of fuzzy solutions of the governing methods are carried out by the approaches, namely Modified Runge Kutta method and Runge Kutta Merson method. The results are compared with the exact solution which is found using generalized Hukuhara derivative (gH-derivative) concepts. Additionally, different illustrative examples and an application in industry of the methods are also undertaken with the useful table and graph to show the usefulness for attained to the proposed approaches.

A Diagonally Implicit Symplectic Runge-Kutta Method with Minimum Phase-lag

2011 ◽  
Author(s):  
Z. Kalogiratou ◽  
Th. Monovasilis ◽  
T. E. Simos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Phase Lag ◽  
Minimum Phase ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

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.

scholarly journals Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
N. A. Ahmad ◽  
N. Senu ◽  
F. Ismail
Keyword(s):  
Numerical Solution ◽  
Numerical Experiments ◽  
Initial Value ◽  
Oscillatory Solutions ◽  
First Order ◽  
Runge Kutta Method ◽  
Algebraic Order ◽  
Runge Kutta ◽  
The Stability ◽  
Order Four

A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK) method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK) methods.

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