• Journal of applied mathematics & informatics
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• v.30 no.5_6
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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.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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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 Chungcheong Mathematical Society
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• v.21 no.4
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• pp.511-517
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• 2008

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

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.879-890
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• 2020

In this paper we study the stability properties of solutions of nonlinear impulsive integro-differential systems by using an integral inequality under the stability of the corresponding variational impulsive integro-differential systems. Also, we give examples to illustrate our results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.1
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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 the Chungcheong Mathematical Society
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• v.13 no.1
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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 the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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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.

• The Pure and Applied Mathematics
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• v.24 no.1
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• pp.1-19
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• 2017

In this paper we obtain some integral inequalities by using Stieltjes derivatives, and we apply our results to the study of asymptotic behavior of a certain second-order integro-differential equation.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.79-87
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• 1995

We complete the proofs of integral and integro-differential inequalities presented in Lakshmikantham, Leela and Raos' results.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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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.