• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.287-296
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• 2007

Using the representation of the solution by means of the resolvent, we study the boundedness of the solutions of some Volterra difference equations.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.321-325
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• 2007

We prove the Medina's results about the existence and uniqueness of solutions of discrete Volterra equations of convolution type in weighted spaces, by using the well-known Contraction Mapping Principle.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.401-409
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• 2010

We study the existence of periodic solutions of Volterra equations by using the limiting equations and contraction mappings.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.163-174
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• 1999

The purpose of this paper is to obtain the solution of Fredholm-Volterra integral equation with singular kernel in the space $L_2(-1, 1)\times C(0,T), 0 \leq t \leq T< \infty$, under certain conditions,. The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrices. Also the error estimate is computed and some numerical examples are computed using the MathCad package.

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

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.323-334
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• 2017

In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.237-244
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• 2006

In this paper, we examine the existence and bounded- ness of the solutions of discrete Volterra equations $$x(n)=f(n)+\sum_{j=0}^{n}g(n,j,x(j))$$, $n{\geq}0$ and $$x(n)=f(n)+\sum_{j=0}^{n}B(n,j)x(j)$$, $n{\geq}0$.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.197-211
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• 2013

We study some stability properties in discrete Volterra equations by employing to change Yoshizawa's results in [13] for the nonlinear equations into results for the nonlinear discrete Volterra equations with unbounded delay.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.463-475
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• 2012

In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.175-183
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• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.