• Journal of applied mathematics & informatics
• /
• v.30 no.5_6
• /
• pp.981-992
• /
• 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
• /
• v.22 no.1
• /
• pp.81-88
• /
• 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
• /
• v.2 no.2
• /
• pp.31-40
• /
• 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
• /
• v.21 no.1
• /
• pp.17-28
• /
• 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
• /
• v.13 no.1
• /
• pp.45-51
• /
• 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
• /
• v.31 no.5_6
• /
• pp.661-667
• /
• 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.

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

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

• Journal of applied mathematics & informatics
• /
• v.9 no.2
• /
• pp.667-677
• /
• 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
• /
• v.56 no.2
• /
• pp.431-450
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.31 no.1_2
• /
• pp.65-77
• /
• 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.