Results 31 to 40 of about 162 (130)

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

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

On the reliable balancing collocation technique for a class of linear two-dimensional Fredholm–Volterra integral equations

Partial Differential Equations in Applied Mathematics, 2022
In this work, a reliable and efficient numerical technique viz. the balancing collocation technique (BCT) has been introduced and employed to solve the linear two-dimensional Fredholm–Volterra integral (F–VI) equations. The technique reduces the solution of these integral equations to the solution of a linear system of algebraic equations. Furthermore,
openaire   +2 more sources

Numerical solution of the nonlinear Fredholm-Volterra- Hammerstein integral equations via Bessel functions

, 2020
In this paper, a collocation method based on the Bessel polynomials is used for the solution of nonlinear Fredholm-Volterra-Hammerstein integral equations (FVHIEs). This method transforms the nonlinear (FVHIEs) into matrix equations with the help of Bessel polynomials of the first kind and collocation points. The matrix equations correspond to a system
Ordokhani, Yadollah, Dehestani, Haniye
openaire   +1 more source

Analysis of the Error in a Numerical Method Used to Solve Nonlinear Mixed Fredholm-Volterra-Hammerstein Integral Equations [PDF]

Journal of Function Spaces and Applications, 2012
This work presents an analysis of the error that is committed upon having obtained the approximate solution of the nonlinear Fredholm-Volterra-Hammerstein integral equation by means of a method for its numerical resolution. The main tools used in the study of the error are the properties of Schauder bases in a Banach space.
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Some Numerical Techniques for Solve Nonlinear Fredholm-Volterra Integral Equation

, 2018
In this paper, the existence and uniqueness of the solution of nonlinear Fredholm – Volterra integral equation is consider(NF-VIE) with continuous kernel , then we use a numerical method to reduce this type of equations to a system of Fredholm integral equation . Trapeziodal rule, Simpson rule, and Romberg integral method are used to solve the Fredholm
A. M. Al-Bugami, J. G. Al-Juaid
openaire   +2 more sources

Fredholm-Volterra integral equation of the first kind with potential kernel

Le Matematiche, 2000
A series method is used to separate the variables of position and time for the Fredholm-Volterra integral equation of the first kind and the solution of the system in L_2 [0,1] × C[0,T], 0 ≤ t ≤ T < ∞ is obtained, the Fredholm integral equation is discussed using Krein's method. The kernel is written in a Legendre polynomial form.
M. H. Fahmy, M. A. Abdou, E. I. Deebs
openaire   +1 more source

An accelerated iterative technique for solving mixed Fredholm-Volterra integral equations

Ain Shams Engineering Journal
In this paper, we propose an accelerated numerical technique for solving mixed Fredholm-Volterra integral equations (MFVIEs). The MFVIE is solved using the two-grid iterative technique, which uses a small system of equations to reach higher accuracy. The convergence analysis showed that using this technique reduces computational costs by 85% compared ...
A.G. Attia, I.L. El-kalla, A. Elsaid, R.A. Abd El-Monem   +3 more
openaire   +2 more sources

Numerical solution for Fredholm–Volterra integral equation of the second kind by using collocation and Galerkin methods

Journal of King Saud University - Science, 2010
AbstractThe Fredholm–Volterra integral equation of the second kind with continuous kernels with respect to position and time, is solved numerically, using the Collocation and Galerkin methods. Also the error, in each case, is estimated.
Hendi, F.A., Albugami, A.M.
openaire   +1 more source

A Fibonacci collocation method for solving a class of Fredholm–Volterra integral equations in two-dimensional spaces

Beni-Suef University Journal of Basic and Applied Sciences, 2014
AbstractIn this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE). The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method
Farshid Mirzaee, Seyede Fatemeh Hoseini
openaire   +2 more sources