Solving fuzzy differential equations using third order Runge Kutta based on contraharmonic mean

New 4(3) pairs Diagonally Implicit Runge-Kutta-Nyström (DIRKN) methods with reduced phase-lag are developed for the integration of initial value problems for second-order ordinary differential equations possessing oscillating solutions. Two DIRKN pairs which are three- and four-stage with high order of dispersion embedded with the third-order formula for the estimation of the local truncation error. These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.

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HISTORY TRACKING ABILITY OF HYBRID SECOND AND FOURTH ORDERS RUNGE-KUTTA IN SOLVING DELAY DIFFERENTIAL EQUATIONS

Jurnal Teknologi ◽

10.11113/jt.v79.9899 ◽

2017 ◽

Vol 79 (6) ◽

Author(s):

Rui Sih Lim ◽

Rohanin Ahmad ◽

Su Hoe Yeak

Keyword(s):

Differential Equations ◽

Numerical Solution ◽

Fourth Order ◽

Delay Differential Equations ◽

Numerical Scheme ◽

Third Order ◽

Acceptable Error ◽

Tracking Ability ◽

Runge Kutta ◽

Delay Differential

This paper presents numerical solution for Delay Differential Equations systems to identify frequent discontinuities which occur after and sometimes before the initial solution. The Runge-Kutta methods have been chosen because they are well-established methods and can be modified to handle discontinuities by means of mapping of past values. The state system of the problem is first discretized before the method is applied to find the solution. Our objective is to develop a scheme for solving delay differential equations using hybrid second and fourth order of Runge-Kutta methods. The results have been compared with the result from Matlab routine dde23 which used second and third order of Runge-Kutta methods. Our numerical scheme is able to successfully handle discontinuities in the system and produces results with acceptable error.

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ANN-based modeling of third order runge kutta method

Journal of Advanced Computer Science & Technology ◽

10.14419/jacst.v4i1.4365 ◽

2015 ◽

Vol 4 (1) ◽

pp. 180

Author(s):

M. Dehghanpour ◽

A. Rahati ◽

E. Dehghanian

Keyword(s):

Differential Equations ◽

Quantum Physics ◽

Numerical Approach ◽

Mathematical Explanation ◽

Kutta Method ◽

Specific System ◽

Third Order ◽

Runge Kutta Method ◽

Numerical Solution Methods ◽

Runge Kutta

<p>The world's common rules (Quantum Physics, Electronics, Computational Chemistry and Astronomy) find their normal mathematical explanation in language of differential equations, so finding optimum numerical solution methods for these equations are very important. In this paper, using an artificial neural network (ANN) a numerical approach is designed to solve a specific system of differential equations such that the training process of the ANN calculates the optimal values for the coefficients of third order Runge Kutta method. To validate our approach, we performed some experiments by solving two body problem using coefficients obtained by ANN and also two other well-known coefficients namely Classical and Heun. The results show that the ANN approach has a better performance in compare with two other approaches.</p>

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