Existence and Uniqueness of the Solution of a System of Integral Equations of the First Kind

2003 ◽  
Vol 39 (9) ◽  
pp. 1263-1270
Author(s):  
A. M. Denisov
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
System Of Integral Equations ◽  
Uniqueness Of The Solution

scholarly journals Determination of an Unknown Coefficient in the Third Order Pseudoparabolic Equation with Non-Self-Adjoint Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yashar T. Mehraliyev ◽  
Gulshan Kh. Shafiyeva
Keyword(s):  
Boundary Conditions ◽  
Classical Solution ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Unknown Coefficient ◽  
Pseudoparabolic Equation ◽  
Third Order ◽  
System Of Integral Equations ◽  
Inverse Boundary ◽  
The Third

The solvability of the inverse boundary problem with an unknown coefficient dependent on time for the third order pseudoparabolic equation with non-self-adjoint boundary conditions is investigated in the present paper. Here we have introduced the definition of the classical solution of the considered inverse boundary value problem, which is reduced to the system of integral equations by the Fourier method. At first, the existence and uniqueness of the solution of the obtaining system of integral equations is proved by the method of contraction mappings; then the existence and uniqueness of the classical solution of the stated problem is proved.

scholarly journals The finite-section approximation for integral equations on the half-line

1987 ◽  
Vol 28 (4) ◽  
pp. 415-434 ◽  
Author(s):  
Frank de Hoog ◽  
Ian H. Sloan
Keyword(s):  
Recent Work ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Half Line ◽  
Asymptotic Bounds ◽  
Novel Technique ◽  
Upper Limit ◽  
Convergence Results ◽  
Finite Section ◽  
Uniqueness Of The Solution

AbstractIntegral equations on the half line are commonly approximated by the finite-section approximation, in which the infinite upper limit is replaced by a positive number β. A novel technique is used here to rederive a number of classical results on the existence and uniqueness of the solution of the Wiener-Hopf and related equations, and is then extended to obtain existence, uniqueness and convergence results for the corresponding finite-section equations. Unlike the methods used in the recent work of Anselone and Sloan, the present methods are constructive, and result in explicit asymptotic bounds for the error introduced by the finite-section approximation.

scholarly journals The Existence and Uniqueness of the Solution of a Nonlinear Fredholm–Volterra Integral Equation with Modified Argument via Geraghty Contractions

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 29
Author(s):  
Maria Dobriţoiu
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Nonlinear Integral Equations ◽  
Uniqueness Of The Solution

Using some of the extended fixed point results for Geraghty contractions in b-metric spaces given by Faraji, Savić and Radenović and their idea to apply these results to nonlinear integral equations, in this paper we present some existence and uniqueness conditions for the solution of a nonlinear Fredholm–Volterra integral equation with a modified argument.

scholarly journals On Solvability of an Inverse Boundary Value Problem for Pseudo Hyperbolic Equation of the Fourth Order

2015 ◽  
Vol 7 (2) ◽  
pp. 101
Author(s):  
Yashar T. Mehraliyev ◽  
Afaq F. Huseynova
Keyword(s):  
Hyperbolic Equation ◽  
Integral Equations ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Fourier Method ◽  
Unknown Coefficient ◽  
Classical Solutions ◽  
Equivalent Problem ◽  
Inverse Boundary ◽  
Uniqueness Of The Solution

We analyze the solvability of the inverse boundary problem with an unknown  coefficient depended on time for the pseudo hyperbolic equation of fourth order with periodic and integral conditions.The initial problem is reduced to an equivalent problem. With the help of the Fourier method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution of the integral equations is proved. The obtained solution of the integral equations is also the only solution to the equivalent problem. Basing on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original problem is proved.

scholarly journals A Sum Operator Method for the Existence and Uniqueness of Positive Solutions to a System of Nonlinear Fractional Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jing Wu ◽  
Tunhua Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Iterative Scheme ◽  
Operator Method ◽  
Quadratic System ◽  
System Of Integral Equations ◽  
Fractional System

This paper is concerned with the existence and uniqueness of positive solutions for a Volterra nonlinear fractional system of integral equations. Our analysis relies on a fixed point theorem of a sum operator. The conditions for the existence and uniqueness of a positive solution to the system are established. Moreover, an iterative scheme is constructed for approximating the solution. The case of quadratic system of fractional integral equations is also considered.

scholarly journals Numerical Method for Fractional Fuzzy Integral Equations

2021 ◽  
Author(s):  
Alexandru Mihai Bica ◽  
Shokrollah Ziari ◽  
Zoltan Satmari
Keyword(s):  
Iterative Method ◽  
Error Estimate ◽  
Numerical Solution ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Uniform Boundedness ◽  
Fuzzy Integral ◽  
Product Integration ◽  
Lipschitz Constants ◽  
Uniqueness Of The Solution

Abstract In the present work we construct an iterative method for the numerical solution of fuzzy fractional Volterra integral equations, by using the technique of fuzzy product integration. The existence and uniqueness of the solution and the uniform boundedness of the terms of the Picard iterations are proved. The convergence of the iterative algorithm is obtained and the apriori error estimate is given in terms of the Lipschitz constants. A numerical example illustrates the accuracy of the method.

scholarly journals Numerical Solution of Two-Dimensional Fredholm–Volterra Integral Equations of the Second Kind

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1326
Author(s):  
Sanda Micula
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Cubature Formula ◽  
Volterra Integral Equations ◽  
Picard Iteration ◽  
Successive Approximations ◽  
Future Research ◽  
Two Dimensional ◽  
Uniqueness Of The Solution

The paper presents an iterative numerical method for approximating solutions of two-dimensional Fredholm–Volterra integral equations of the second kind. As these equations arise in many applications, there is a constant need for accurate, but fast and simple to use numerical approximations to their solutions. The method proposed here uses successive approximations of the Mann type and a suitable cubature formula. Mann’s procedure is known to converge faster than the classical Picard iteration given by the contraction principle, thus yielding a better numerical method. The existence and uniqueness of the solution is derived under certain conditions. The convergence of the method is proved, and error estimates for the approximations obtained are given. At the end, several numerical examples are analyzed, showing the applicability of the proposed method and good approximation results. In the last section, concluding remarks and future research ideas are discussed.

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