Results 101 to 110 of about 3,901 (233)

An Effective Method for Solving Fractional Integrodifferential Equations of the Volterra and Fredholm Types Based on the Lucas Polynomials

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This article extends a spectral collocation approach based on Lucas polynomials to numerically solve the integrodifferential equations of both Volterra and Fredholm types for multi–higher fractional order in the Caputo sense under the mixed conditions. The new approach focusses on using a matrix strategy to convert the supplied equation with conditions
Shabaz Jalil Mohammedfaeq, Miran Bayan Mohammed Amin, Dashne Chapuk Zahir, Shazad Shawki Ahmed, Saeid Abbasbandy   +4 more
wiley   +1 more source

Generalized Bihari Type Integral Inequalities and the Corresponding Integral Equations

Journal of Inequalities and Applications, 2009
We study some special nonlinear integral inequalities and the corresponding integral equations in measure spaces. They are significant generalizations of Bihari type integral inequalities and Volterra and Fredholm type integral equations.
László Horváth
doaj   +2 more sources

A Product Integration type Method for solving Nonlinear Integral Equations in L

, 2016
This paper deals with nonlinear Fredholm integral equations of the second kind. We study the case of a weakly singular kernel and we set the problem in the space L 1 ([a, b], C). As numerical method, we extend the product integration scheme from C 0 ([a,
Ahues, M., Grammont, L., Kaboul, H.
core   +5 more sources

Analyze Second‐Order PDEs Using the Volterra–Fredholm Integral Equation

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this study, we propose a novel approach to address a particular second‐order partial differential equation along with its boundary value conditions (SPDEs). In this process, we transfer the SPDEs problem into Volterra–Fredholm integral equation (VFIE), and we perform the Tau method bases on orthogonal Legendre polynomials directly, for solution of ...
Choonkil Park, Javad Shokri, Richard I. Avery   +2 more
wiley   +1 more source

An Analytical‐Numerical Method for the Solution of Nonlinear Fractional Fredholm Integro‐Differential Equations With Logarithmic Weakly Singular Kernel

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this work, we investigate a numerical method for solving nonlinear fractional Fredholm integro‐differential equations with logarithmic weakly singular kernels. Since the direct solution of these equations using classical methods results in low accuracy and high computational cost due to the singular behavior of the exact solution at both endpoints ...
Ali Edham Awadh, Esmaeil Najafi, Guotao Wang   +2 more
wiley   +1 more source

Existence and Uniqueness Theorem of Fractional Mixed Volterra-Fredholm Integrodifferential Equation with Integral Boundary Conditions

International Journal of Differential Equations, 2011
We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
Shayma Adil Murad, Hussein Jebrail Zekri, Samir Hadid   +2 more
doaj   +1 more source

An Analytical Approach to Solve a System of 2D Nonlinear Volterra–Fredholm Integral Equations on Nonrectangular Domains Based on Radial Basis Functions

Journal of Mathematics, Volume 2025, Issue 1, 2025.
We aim to introduce a numerical method to solve a system of two‐dimensional nonlinear integral equations of Volterra–Fredholm type with the second kind on nonrectangular domains. The method estimates the solutions of the system by a discrete collocation method based on radial basis functions constructed on scattered points.
Mohsen Jalalian, Manochehr Kazemi, Mohammad Esmael Samei, Chang Phang   +3 more
wiley   +1 more source

Posteriori error estimates for the nonlinear Volterra-Fredholm integral equations

Computers & Mathematics with Applications, 2003
The central object of study in the paper under review is the general nonlinear Volterra-Fredholm integral equation and its numerical treatment. \textit{S. Kumar} and \textit{I. H. Sloan} [Math. Comp. 48, 585--593 (1987; Zbl 0616.65142)] introduced an approach to convert the conventional Hammerstein integral equation into a conductive form for ...
openaire   +1 more source

Haar Wavelet Method for the System of Integral Equations

Abstract and Applied Analysis, 2014
We employed the Haar wavelet method to find numerical solution of the system of Fredholm integral equations (SFIEs) and the system of Volterra integral equations (SVIEs).
Hassan A. Zedan, Eman Alaidarous
doaj   +1 more source

New Perturbation Iteration Solutions for Fredholm and Volterra Integral Equations

Journal of Applied Mathematics, 2013
In this paper, recently developed perturbation iteration method is used to solve Fredholm and Volterra integral equations. The study shows that the new method can be applied to both types of integral equations.
İhsan Timuçin Dolapçı, Mehmet Şenol, Mehmet Pakdemirli   +2 more
doaj   +1 more source