In this paper, Adomian decomposition method (ADM) and homotopy analysis method (HAM) are proposed to solving the fuzzy nonlinear Volterra-Fredholm integral equation of the second kind(FV FIE− 2). we convert a fuzzy nonlinear Volterra-Fredholm integral equation to a nonlinear system of Volterra-Fredholm integral equation in crisp case. we use ADM , HAM and find the approximate solution of this s...

In this paper, we propose a successive approximation method based on fuzzy wavelet like operator to approximate the solution of linear fuzzy Fredholm integral equations of the second kind with arbitrary kernels. We give the convergence conditions and an error estimate. Also, we investigate the numerical stability of the computed values with respect to small perturbations in the first iteration....

We study the parametrized Hamiltonian action functional for finitedimensional families of Hamiltonians. We show that the linearized operator for the L2-gradient lines is Fredholm and surjective, for a generic choice of Hamiltonian and almost complex structure. We also establish the Fredholm property and transversality for generic S1-invariant families of Hamiltonians and almost complex structur...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

Ahmed A. Hamoud, Nedal M. Mohammed, Homan Emadifar;, Foroud Parvaneh, Faraidum K. Hamasalh, Soubhagya Kumar Sahoo, and Masoumeh Khademi. International Journal of Fuzzy Logic Intelligent Systems 2022;22:391-400. https://doi.org/10.5391/IJFIS.2022.22.4.391

We propose several approaches to the numerical solution of a new Fredholm integro-differential equations modelling neural networks. A solution strategy based on expansions onto standard cardinal basis functions and collocation is presented. Comparative numerical experiments illustrate specific advantages and drawbacks of the different approaches and are used to motivate alternate strategies. 20...

In this study, a Taylor method is developed for numerically solving the high-order most general nonlinear Fredholm integro-differential-difference equations in terms of Taylor expansions. The method is based on transferring the equation and conditions into the matrix equations which leads to solve a system of nonlinear algebraic equations with the unknown Taylor coefficients. Also, we test the ...

This paper presents a ε-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, finite difference is established on non-uniform mesh by using interpolating quadrature rules linear basis functions. An error analysis successfully carried out Boglaev–Bakhvalov-type mesh....