• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.699-721
• /
• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.165-182
• /
• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.7 no.2
• /
• pp.65-73
• /
• 2003

In this work, we use a numerical method to solve the nonlinear integral equation of the second kind when the kernel of the integral equation in the logarithmic function form or in Carleman function form. The solution has a computing time requirement of $0(N^2)$, where (2N +1) is the number of discretization points used. Also, the error estimate is computed.

• Kyungpook Mathematical Journal
• /
• v.60 no.4
• /
• pp.869-881
• /
• 2020

Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.

• Bulletin of the Korean Mathematical Society
• /
• v.42 no.4
• /
• pp.789-805
• /
• 2005

In this paper we consider analogous of Gronwall-type inequalities involving iterated integrals in the inequality (1.2) for functions when the function u in the right-hand side of the in­equality (1.2) is replaced by the function $u^P$ for some p. These inequalities are effective tools in the study of a system of an integral equation. We also provide some integral inequalities involving iterated integrals.

• Communications of the Korean Mathematical Society
• /
• v.13 no.4
• /
• pp.811-815
• /
• 1998

In this paper we define a sample path-valued conditional Yeh-Wiener integral for function F of the type E[F(x)$\mid$x(*,(equation omitted))=$\psi({\blacktriangle})]$, where $\psi$ is in C[0, (equation omitted)] and ${\blacktriangle}$ = (equation omitted) and evaluate a sample path-valued conditional Yeh-Wiener integral using the result obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.2
• /
• pp.67-80
• /
• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.223-236
• /
• 2000

In this paper, we solve the Fredholm integral equation of the first and second kind when the kernel takes a singular form. Also, some important relations for Chebyshev polynomial of integration are established.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.1
• /
• pp.111-123
• /
• 2005

Here, the Fredholm integral equation with Hilbert kernel is solved numerically, using two different methods. Also the error, in each case, is estimated.

• Coupled systems mechanics
• /
• v.1 no.2
• /
• pp.183-204
• /
• 2012

A method for the analysis of wave scattering in 3-D elastic full space is developed by means of the coupled boundary-volume integral equation, which takes into account the effects of both the boundary of inclusions and the uctuation of the wave field. The wavenumber domain formulation is used to construct the Krylov subspace by means of FFT. In order to achieve the wavenumber domain formulation, the boundary-volume integral equation is transformed into the volume integral equation. The formulation is also focused on this transform and its numerical implementation. Several numerical results clarify the accuracy and effectiveness of the present method for scattering analysis.