A parameter uniform difference scheme for the parameterized singularly perturbed problem with integral boundary condition

Kudu, Mustafa

doi:10.1186/s13662-018-1620-0

Cited by 20 publications

(7 citation statements)

References 35 publications

(70 reference statements)

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“…This part presents some preliminaries and notations of FC. There are numerous definitions of derivative and integration are available in litrature [29][30][31][32][33][34][35][36][37][38][39][40][41]. It is well known by the several published research papers that the Caputo and RL definitions are most popular definition of fractional calculus.…”

Section: Fractional Calculusmentioning

confidence: 99%

An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets

et al. 2020

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In this paper, the operational matrix based on Bernstein wavelets is presented for solving fractional SIR model with unknown parameters. The SIR model is a system of differential equations that arises in medical science to study epidemiology and medical care for the injured. Operational matrices merged with the collocation method are used to convert fractional-order problems into algebraic equations. The Adams–Bashforth–Moulton predictor correcter scheme is also discussed for solving the same. We have compared the solutions with the Adams–Bashforth predictor correcter scheme for the accuracy and applicability of the Bernstein wavelet method. The convergence analysis of the Bernstein wavelet has been also discussed for the validity of the method.

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Section: Fractional Calculusmentioning

confidence: 99%

An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets

et al. 2020

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“…Remark To the author's knowledge, the issue of antiperiodic RNNs involving proportional delays has never been investigated. Obviously, the corresponding conclusions in Shao, Tan, Gong, Cao, Li, Zhou, Yang, Wang, Peng and Wang, Cai et al, Li et al, Kudu, Hu et al, Hu and Zou, Huang et al, and Hu et al and the references cited therein cannot be used to deal with the exponential convergence on the

π

antiperiodic phenomenon for system .…”

Section: Numerical Example and Simulationsmentioning

confidence: 99%

Stability of antiperiodic recurrent neural networks with multiproportional delays

Huang

Long

Cao

2020

Math Methods in App Sciences

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In general, a proportional function is obviously not antiperiodic, yet a very interesting fact in this paper shows that it is possible there is an antiperiodic solution for some proportional delayed dynamical systems. We deal with the issue of antiperiodic solutions for RNNs (recurrent neural networks) incorporating multiproportional delays. Employing Lyapunov method, inequality techniques and concise mathematical analysis proof, sufficient criteria on the existence of antiperiodic solutions including its uniqueness and exponential stability are built up. The obtained results provide us some lights for designing a stable RNNs and complement some earlier publications. In addition, simulations show that the theoretical antiperiodic dynamics are in excellent agreement with the numerically observed behavior. KEYWORDSantiperiodic, proportional delay, recurrent neural network, stability MSC CLASSIFICATION 34C25; 34K13; 34K25Math Meth Appl Sci. 2020;43:6093-6102.wileyonlinelibrary.com/journal/mma

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“…Special techniques, in which the error is independent of the perturbation parameter, are required to obtain a good numerical approximations to such problems. In a recent years, there has been a surge in interest for solving singularly perturbed differential equations with integral boundary conditions [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Hybrid numerical method for solving singularly perturbed partial delay reaction-diffusion problem with integral boundary condition

Wondimu

Duressa

Woldaregay

et al. 2023

Preprint

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In this paper, we study the numerical method for solving singularly perturbed partial delay differential equations with integral boundary conditions. Due to a small perturbation parameter acted on the higher derivative, solution of the problem exhibit a boundary layers at left and right end plane of the domain. An interior layer is also formed because of the presence of large delay on the space variable. A hybrid numerical method is proposed in the spatial direction, and an implicit Euler method is used in temporal direction. The proposed hybrid scheme constitute of cubic spline method in the boundary layer region and a classical finite difference method in the outer layer region. The integral boundary condition is treated using Simpson’s 1/3 rule. The uniform stability and convergence analysis for the proposed scheme is studied. The developed method is uniformly convergent with second-order in space and first-order in time. Two numerical test examples are considered to validate a theoretical result. The numerical results are in agreement with the theoretical estimations. MSC Classification: 65M06 , 65M12 , 65M22 , 65M25

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A parameter uniform difference scheme for the parameterized singularly perturbed problem with integral boundary condition

Cited by 20 publications

References 35 publications

An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets

An Efficient Numerical Method for Fractional SIR Epidemic Model of Infectious Disease by Using Bernstein Wavelets

Stability of antiperiodic recurrent neural networks with multiproportional delays

Hybrid numerical method for solving singularly perturbed partial delay reaction-diffusion problem with integral boundary condition

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