scholarly journals Numerical solution of generalized fractional Volterra integro-differential equations via approximation the Bromwich integral

2021 ◽  
Vol 2090 (1) ◽  
pp. 012131
Author(s):  
Shiva Eshaghi ◽  
Yadollah Ordokhani
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Complex Plane ◽  
Numerical Scheme ◽  
Optimal Contour ◽  
Bromwich Integral

Abstract In this paper, we consider the generalized fractional Volterra integro-differential equations with the regularized Prabhakar derivative and represent the solution of this type of equations in the form of Bromwich integral in the complex plane. Then we select the hyperbolic contour as an optimal contour to approximate the Bromwich integral. Further, an example to show absolute errors for various parameters by using our numerical scheme on hyperbolic contour is given.

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

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.

Numerical solution of fractal-fractional Mittag–Leffler differential equations with variable-order using artificial neural networks

2021 ◽  
Author(s):  
C. J. Zúñiga-Aguilar ◽  
J. F. Gómez-Aguilar ◽  
H. M. Romero-Ugalde ◽  
R. F. Escobar-Jiménez ◽  
G. Fernández-Anaya ◽  
...  
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Differential Equations ◽  
Numerical Solution ◽  
Variable Order ◽  
Artificial Neural
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