An Iterative Scheme for Solving Arbitrary-Order Nonlinear Volterra Integro-Differential Equations Involving Delay

Ghosh, Bappa; Mohapatra, Jugal

doi:10.1007/s40995-023-01446-2

Cited by 9 publications

(2 citation statements)

References 27 publications

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“…A specific type of time-delay system is the so-called Volterra system [1,2,18,19]. It can be pointed out that Volterra integro-differential equations exhibit dynamics of distributed delay type under the form of convolution or non-convolution integral contributions on each whole time interval previous to the time current instant where the solution is calculated.…”

Section: Introductionmentioning

confidence: 99%

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A Study of the Stability of Integro-Differential Volterra-Type Systems of Equations with Impulsive Effects and Point Delay Dynamics

De la Sen

2024

Mathematics

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This research relies on several kinds of Volterra-type integral differential systems and their associated stability concerns under the impulsive effects of the Volterra integral terms at certain time instants. The dynamics are defined as delay-free dynamics contriobution together with the contributions of a finite set of constant point delay dynamics, plus a Volterra integral term of either a finite length or an infinite one with intrinsic memory. The global asymptotic stability is characterized via Krasovskii–Lyapuvov functionals by incorporating the impulsive effects of the Volterra-type terms together with the effects of the point delay dynamics.

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Section: Introductionmentioning

confidence: 99%

“…It can be pointed out that Volterra integro-differential equations exhibit dynamics of distributed delay type under the form of convolution or non-convolution integral contributions on each whole time interval previous to the time current instant where the solution is calculated. See, for instance [1,18,19] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A Study of the Stability of Integro-Differential Volterra-Type Systems of Equations with Impulsive Effects and Point Delay Dynamics

De la Sen

2024

Mathematics

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A higher order stable numerical approximation for time‐fractional non‐linear Kuramoto–Sivashinsky equation based on quintic B‐‐spline

Choudhary,

Singh,

Das

et al. 2024

Math Methods in App Sciences

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This article deals with designing and analyzing a higher order stable numerical analysis for the time‐fractional Kuramoto–Sivashinsky (K‐S) equation, which is a fourth‐order non‐linear equation. The fractional derivative of order present in the considered problem is taken into Caputo sense and approximated using the scheme. In space direction, the discretization process uses quintic ‐spline functions to approximate the derivatives and the solution of the problem. The present approach is unconditionally stable and is convergent with rate of accuracy , where and denote the space and time step sizes, respectively. We have also noted that the linearized version of the K‐S equation leads the rate of accuracy to . The present approach is also highly effective for the time‐fractional Burgers' equation. We have shown that the present approach provides better accuracy than the scheme with the same computational cost for several linear/non‐linear problems, with classical as well as fractional time derivatives.

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A numerical approach for singularly perturbed reaction diffusion type Volterra-Fredholm integro-differential equations

Durmaz

2023

J. Appl. Math. Comput.

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An Iterative Scheme for Solving Arbitrary-Order Nonlinear Volterra Integro-Differential Equations Involving Delay

Cited by 9 publications

References 27 publications

A Study of the Stability of Integro-Differential Volterra-Type Systems of Equations with Impulsive Effects and Point Delay Dynamics

A Study of the Stability of Integro-Differential Volterra-Type Systems of Equations with Impulsive Effects and Point Delay Dynamics

A higher order stable numerical approximation for time‐fractional non‐linear Kuramoto–Sivashinsky equation based on quintic B‐‐spline

A numerical approach for singularly perturbed reaction diffusion type Volterra-Fredholm integro-differential equations

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