• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

• Korean Journal of Mathematics
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• 제25권3호
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• pp.303-321
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• 2017

In this paper we use the Krasnoselskii-Burton's fixed point theorem to obtain asymptotic stability and stability results about the zero solution for the following nonlinear neutral Levin-Nohel integro-differential equation $$x^{\prime}(t)+{\displaystyle\smashmargin{2}{\int\nolimits_{t-{\tau}(t)}}^t}a(t,s)g(x(s))ds+c(t)x^{\prime}(t-{\tau}(t))=0$$. The results obtained here extend the work of Mesmouli, Ardjouni and Djoudi [20].

• 충청수학회지
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• 제32권4호
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• pp.409-420
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• 2019

In this article, we discussed semi-analytical approximated methods for solving mixed Volterra-Fredholm integro-differential equations, namely: Adomian decomposition method and modified Adomian decomposition method. Moreover, we prove the uniqueness results and convergence of the techniques. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.197-208
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• 2024

In the present paper, we establish Ulam-Hyres and Ulam-Hyers-Rassias stabilities for nonlinear impulsive integro-differential equations with non-local condition in Banach space. The generalization of Grownwall type inequality is used to obtain our results.

• 충청수학회지
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• 제20권4호
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• pp.561-568
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• 2007

In this paper, we improve the results of [9] and give an application to boundedness of the solutions of nonlinear integro-differential equations.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.807-816
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• 2014

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 추계학술대회 학술발표 논문집
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• pp.58-63
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• 1998

We will prove the existence and uniqueness theorem of solutions to the nonlocal fuzzy integro-differential equations using Contraction mapping principle.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제4권1호
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• pp.40-44
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• 2004

In this paper we study the existence and uniqueness of fuzzy solutions for the nonlinear fuzzy integro-differential equations on $E^{n}_{N}$ by using the concept of fuzzy number of dimension n whose values are normal, convex, upper semicontinuous and compactly supported surface in $E^{n}_{N}$. $E^{n}_{N}$ be the set of all fuzzy numbers in $R^{n}$ with edges having bases parallel to axis $x_1$, $x_2$, …, $x_n$.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.189-201
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• 2022

The aim of the current work is to investigate the numerical study of a nonlinear Volterra-Fredholm integro-differential equation with initial conditions. Our approximation techniques modified adomian decomposition method (MADM) and variational iteration method (VIM) are based on the product integration methods in conjunction with iterative schemes. The convergence of the proposed methods have been proved. We conclude the paper with numerical examples to illustrate the effectiveness of our methods.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권1호
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• pp.19-38
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• 2006

We analyze the spectral collocation approximation for a parabolic partial integrodifferential equations(PIDE) with a weakly singular kernel. The space discretization is based on the spectral collocation method and the time discretization is based on Crank-Nicolson scheme with a graded mesh. We obtain the stability and second order convergence result for fully discrete scheme.