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

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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Numerical Solution of Fuzzy Initial Value Problems by Fourth Order Runge-Kutta Method Based on Contraharmonic Mean

Indian Journal Of Applied Research ◽

10.15373/2249555x/apr2013/111 ◽

2011 ◽

Vol 3 (4) ◽

pp. 59-63 ◽

Cited By ~ 1

Author(s):

R. Gethsi Sharmila ◽

◽

E. C. Henry Amirtharaj

Keyword(s):

Numerical Solution ◽

Fourth Order ◽

Initial Value Problems ◽

Kutta Method ◽

Initial Value ◽

Runge Kutta Method ◽

Contraharmonic Mean ◽

Runge Kutta

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On a parallel mesh-chopping algorithm for a class of initial value problems using fourth-order explicit Runge-Kutta method

Applied Mathematics and Computation ◽

10.1016/s0096-3003(02)00393-4 ◽

2003 ◽

Vol 143 (2-3) ◽

pp. 565-570 ◽

Cited By ~ 1

Author(s):

C.P Katti ◽

D.K Srivastava

Keyword(s):

Fourth Order ◽

Initial Value Problems ◽

Kutta Method ◽

Initial Value ◽

Runge Kutta Method ◽

Runge Kutta

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

Mathematical Problems in Engineering ◽

10.1155/2017/1871278 ◽

2017 ◽

Vol 2017 ◽

pp. 1-11 ◽

Cited By ~ 3

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

International Journal of Scientific Research in Science Engineering and Technology ◽

10.32628/ijsrset196142 ◽

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.

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