• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.981-992
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• 2012

Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed to solving such equations. We introduce the NHPM for solving nonlinear integro-differential equations. Several examples for solving integro-differential equations are presented to illustrate the efficiency of the proposed NHPM.

• 충청수학회지
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• 제22권1호
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• pp.81-88
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• 2009

In this paper, we investigate h-stability for the nonlinear Volterra integro-differential equations and the functional integro-differential equations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.31-40
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• 1998

Spectral analysis by energy method is given for a fully discrete methods for hyperbolic integro-differential equations with a weakly singular kernel. Stability and error estimates in $H^1$-norm are derived.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권1호
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• pp.17-28
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• 2017

A combined form of the modified Laplace Adomian decomposition method (LADM) is developed for the analytic treatment of the nonlinear Volterra-Fredholm integro differential equations. This method is effectively used to handle nonlinear integro differential equations of the first and the second kind. Finally, some examples will be examined to support the proposed analysis.

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.899-913
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• 2024

In this article, the Series Solution Method (SSM) is employed to solve the linear or non-linear Volterra integro-differential equations. Numerous examples have been presented to explain the numerical results, which is the comparison between the exact solution and the numerical solution, and it is found through the tables. The amount of error between the exact solution and the numerical solution is very small and almost nonexistent, and it is also illustrated through the graph how the exact solution completely applies to the numerical solution. This proves the accuracy of the method, which is the Series Solution Method (SSM) for solving the linear or non-linear Volterra integro-differential equations using Mathematica. Furthermore, this approach yields numerical results with remarkable accuracy, speed, and ease of use.

• 충청수학회지
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• 제13권1호
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• pp.45-51
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• 2000

We will investigate some properties of integro-delay-differential equations, $$x^{\prime}(t)=A(t)x(t-g_1(t,x_t))+{\int}_{t_0}^{t}B(t,s)x(s-g_2(s,x_s))ds,\;t_0{\geq}0,\\x(t_0)={\phi}$$,

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.661-667
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• 2013

In this paper we propose the iterated projection method for the approximate solution of an integro-differential equations with Cauchy kernel in $L^2([-1,1],\mathbb{C})$ using Legendre polynomials. We prove the convergence of the method. A system of linear equations is to be solved. Numerical examples illustrate the theoretical results.

• 충청수학회지
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• 제21권4호
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• pp.511-517
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• 2008

In this paper, we investigate h-stability of nonlinear integro-differential equations.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.667-677
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• 2002

In this paper we obtain the matrix Tau Method representation of a general boundary value problem for Fredholm and Volterra integro-differential equations of order $\nu$. Some theoretical results are given that simplify the application of the Tau Method. The application of the Tau Method to the numerical solution of such problems is shown. Numerical results and details of the algorithm confirm the high accuracy and user-friendly structure of this numerical approach.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.431-450
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• 2016

In this paper, the existence, uniqueness, stability via continuous dependence and Ulam stabilities of nonlinear integro-differential equations with random impulses are studied under sufficient condition. The results are obtained by using Leray-Schauder alternative fixed point theorem and Banach contraction principle.