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

• Korean Journal of Mathematics
• /
• v.25 no.3
• /
• pp.323-334
• /
• 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 applied mathematics & informatics
• /
• v.7 no.2
• /
• pp.575-583
• /
• 2000

In this work, we solve the Fredholm-Volterra integral equation(FVIE) when the kernel takes a potential function form under given conditions. we represent this kernel in the Weber-sonin integral form.

• 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.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.1
• /
• pp.259-273
• /
• 2024

In this manuscript, we study the sufficient conditions for existence and uniqueness results of solutions of impulsive Hilfer fractional Volterra-Fredholm integro-differential equations with integral boundary conditions. Fractional calculus and Banach contraction theorem used to prove the uniqueness of results. Moreover, we also establish Hyers-Ulam stability for this problem. An example is also presented at the end.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.869-885
• /
• 2021

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.1
• /
• pp.237-249
• /
• 2023

In this paper, by means of the Schauder fixed point theorem and Arzela-Ascoli theorem, the existence and uniqueness of solutions for a class of not instantaneous impulsive problems of nonlinear fractional functional Volterra-Fredholm integro-differential equations are investigated. An example is given to illustrate the main results.