Results 61 to 70 of about 3,012,051 (188)

Spline‐Based Computational Technique for Singularly Perturbed Fredholm Integro‐Differential Problems

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
In this work, using a spline‐based discretization, we develop a computational approach for singularly perturbed Fredholm integro‐differential equations. The scheme addresses the challenges of the singular perturbation parameter ϵ through a tension and compression spline technique, coupled with Simpson’s rule for quadrature approximations.
Rajagopal S., Dinesh Kumar S., Patricia J. Y. Wong   +2 more
wiley   +1 more source

Legendre multi-wavelets collocation method for numerical solution of linear and nonlinear integral equations

Alexandria Engineering Journal, 2020
In this article, a new collocation technique for numerical solution of Fredholm, Volterra and mixed Volterra-Fredholm integral equations of the second kind is introduced and also developed a numerical integration formula on the basis of linear Legendre ...
Muhammad Asif, Imran Khan, Nadeem Haider, Qasem Al-Mdallal   +3 more
doaj   +1 more source

Some Solutions of Hilfer Fractional Volterra Integral Equations by Using Pathway‐Type Transform

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
The Pathway‐type Pε‐transform technique has been introduced as a versatile binomial transform encompassing various classes, including the classical Laplace transform. In this paper, we apply this technique to derive solutions for fractional Volterra integral equations (FVIEs) and fractional Abel–Volterra integral equations (FAVIEs) that involve Hilfer ...
Faten H. Damag, Mohammad Alshammari, Amin Saif, Mohammed S. Alsharafi, Adem Kilicman, Shikha Binwal   +5 more
wiley   +1 more source

A Lucas Operational Matrix Method for Solving Nonlinear Fractional Two‐Dimensional Partial Volterra Integral Equations

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This paper introduces a new numerical method for solving a class of two‐dimensional fractional partial Volterra integral equations (2DFPVIEs). Our approach uses Lucas polynomials (LPs) to construct operational matrices (OMs) that effectively transform the complex fractional‐order equations into a more manageable system of algebraic equations.
S. S. Gholami, A. Ebadian, A. A. Khajehnasiri, Kareem T. Elgindy, Birendra Nath Mandal   +4 more
wiley   +1 more source

An Algorithm for the Solution of Nonlinear Volterra–Fredholm Integral Equations with a Singular Kernel

Fractal and Fractional, 2023
The nonlinear Volterra–Fredholm integral Equation (NVFIE) with a singular kernel is discussed such that the kernel of position can take the Hilbert kernel form, Carleman function, logarithmic form, or Cauchy kernel. Using the quadrature method, the NVFIE
Sahar M. Abusalim, Mohamed A. Abdou, Mohamed E. Nasr, Mohamed A. Abdel-Aty   +3 more
doaj   +1 more source

Computational Framework for Numerical Simulation of Fractional‐Order Financial Crime Model via Lucas Collocation Technique

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
The Lucas collocation approach is used in this study to approximate a fractional‐order financial crime model (FOFCM) numerically. The model categorizes the population into five groups: persons without a financial criminal past, those inclined toward financial crimes, active participants, individuals undergoing prosecution, and those imprisoned.
Mahmoud Abd El-Hady, Homan Emadifar, Mehdi Hariri, Atallah El-Shenawy, Chong Lin   +4 more
wiley   +1 more source

Volterra integral equations solved in Fredholm form using Walsh functions [PDF]

, 2004
Recently Walsh function methods have been developed for the numerical solution of several classes of problems, mainly linear and nonlinear integral equations of both Volterra and Fredholm types.
May, R. L., Widyaningsih, P., Blyth, W. F.   +2 more
core   +1 more source

Estimation on solutions of a class of generalized nonlinear Volterra-Fredholm type integral inequalities with applications

上海师范大学学报. 自然科学版, 2015
We establish a class of new nonlinear retarded Volterra-Fredholm type integral inequalities, where a known function σ1(s) in integral functions in [Ma, QH, Peˇcari´c, J: Estimates on solutions of some new nonlinear retarded Volterra-Fredholm type ...
WANG Wusheng, ZHOU Xiaoliang
doaj   +1 more source

On the Multiwavelets Galerkin Solution of the Volterra–Fredholm Integral Equations by an Efficient Algorithm

Journal of Mathematics, 2020
We develop the multiwavelet Galerkin method to solve the Volterra–Fredholm integral equations. To this end, we represent the Volterra and Fredholm operators in multiwavelet bases.
H. Bin Jebreen
doaj   +1 more source

A NUMERICAL SOLUTION OF NONLINEAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS

Journal of Applied Analysis & Computation, 2013
In this paper, a numerical procedure for solving a class ofnonlinear Volterra-Fredholm integral equations is presented. Themethod is based upon the globally defined sinc basis functions.Properties of the sinc procedure are utilized to reduce thecomputation of the nonlinear integral equations to some algebraicequations.
openaire   +1 more source