Volterra–Fredholm integral equation of the first kind and spectral relationships

Abdou, M. A.; Salama, F. A.

doi:10.1016/s0096-3003(03)00619-2

Cited by 12 publications

(7 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to the previous lemmas, by Schauder fixed point theorem, see [19][20], ̅ has at least one fixed point in , and Theorem 1 is proved. (12) where it satisfies the condition in Eq. 7.…”

Section: Introductionmentioning

confidence: 99%

Solution of Integral Equation in Two-Dimensional using Spectral Relationships

Alharbi¹

2020

GJCST

View full text Add to dashboard Cite

This paper concerned using spectral relationships in the solution of the integral equation (IE) in two-dimensional. To discuss that, the (IE) in two-dimensional under certain conditions was considered. The existence of at least one solution of the (IE) was discussed by proving the continuity and compactness of an integral operators. Chebyshev polynomials of the first kind were used to transform the (IE) to a linear algebraic system. Many numerical results and estimating errors were calculated and plotted by the Maple program in different cases.

show abstract

Section: Introductionmentioning

confidence: 99%

Solution of Integral Equation in Two-Dimensional using Spectral Relationships

Alharbi¹

2020

GJCST

View full text Add to dashboard Cite

show abstract

“…(3) If,in (1.3), 0   , we have a MIE of the first kind, where [14] many spectral relationshipsare obtained in [14] In addition the work of Abdou et al,in [15][16][17] is considered special cases of this work In order to guarantee the existence of a unique solution of the linear equation (1.1), we assume the following conditions: (i) The kernel ofposition satisfies the discontinuity condition…”

Section: Introductionmentioning

confidence: 99%

General Formula of Linear Mixed Integral Equation with Weak Singular Kernel

El-Rahman¹

2016

IOSR

View full text Add to dashboard Cite

In this paper, we consider a mixed integral equation (MIE) of the second kind. Under certain conditions, the existence of a unique solution of is discussed and proved. The kernel of position takes asingular form, while the kernel of time is continuous. Using a quadratic numerical method, the MIE leads us to a linear system of Fredholm integral equations (SFIEs). Then,SFIEsafter using Toeplitz matrix method (TMM),tends to a linear algebraic system (LAS). The existence of a unique solution of LAS is proved. Finally, numerical examples are considered, and the error, in each case, is calculated.

show abstract

“…In Ref. [5], EL-Borai et al studied the existence and uniqueness of solution of nonlinear IE of the second kind. Abdou and Salama, in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Abdou and Salama, in Ref. [5], obtained the solution in one, two and three dimensions for the V-FIT of the first kind using spectral relationships. In Ref.…”

Section: Introductionmentioning

confidence: 99%

On Numerical Solution Approach for the Volterra-Fredholm Integral Equation

Ismail

Khamis

Abdou

et al. 2015

j comput theor nanosci

View full text Add to dashboard Cite

In this paper, authors discussed the existence of a unique solution of Volterra-Fredholm integral equation of second kind in the space L p × C 0 T with a generalized kernel, in the domain of integration of several spaces, and t ∈ 0 T is the time is considered. A numerical technique used to obtain a system of Fredholm integral equations, Also authors considered the existence and the uniqueness of the system of equations. Moreover, the Toeplitz matrix method and Product Nystrom method are used to obtain numerically the solution of Fredholm integral equations with logarithmic kernel and Carleman function. Many special cases are considered and established from the work.

show abstract

Volterra–Fredholm integral equation of the first kind and spectral relationships

Cited by 12 publications

References 12 publications

Solution of Integral Equation in Two-Dimensional using Spectral Relationships

Solution of Integral Equation in Two-Dimensional using Spectral Relationships

General Formula of Linear Mixed Integral Equation with Weak Singular Kernel

On Numerical Solution Approach for the Volterra-Fredholm Integral Equation

Contact Info

Product

Resources

About