The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Mohsen Razzaghi - One of the best experts on this subject based on the ideXlab platform.
-
a composite collocation method for the nonlinear mixed volterra Fredholm hammerstein integral equations
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: Hamid Reza Marzban, Mohsen Razzaghi, H R TabrizidoozAbstract:Abstract This paper presents a computational technique for the solution of the nonlinear mixed Volterra–Fredholm–Hammerstein integral equations. The method is based on the composite collocation method. The properties of hybrid of block-pulse functions and Lagrange polynomials are discussed and utilized to define the composite interpolation operator. The estimates for the errors are given. The composite interpolation operator together with the Gaussian integration formula are then used to transform the nonlinear mixed Volterra–Fredholm–Hammerstein integral equations into a system of nonlinear equations. The efficiency and accuracy of the proposed method is illustrated by four numerical examples.
-
semiorthogonal spline wavelets approximation for Fredholm integro differential equations
Mathematical Problems in Engineering, 2006Co-Authors: Mehrdad Lakestani, Mohsen Razzaghi, Mehdi DehghanAbstract:A method for solving the nonlinear second-order Fredholm integro-differential equations is presented. The approach is based on a compactly supported linear semiorthogonal B-spline wavelets. The operational matrices of derivative for B-spline scaling functions and wavelets are presented and utilized to reduce the solution of Fredholm integro-differential to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
-
legendre wavelets method for the nonlinear volterra Fredholm integral equations
Mathematics and Computers in Simulation, 2005Co-Authors: S A Yousefi, Mohsen RazzaghiAbstract:A numerical method for solving the nonlinear Volterra-Fredholm integral equations is presented. The method is based upon Legendre wavelet approximations. The properties of Legendre wavelet are first presented. These properties together with the Gaussian integration method are then utilized to reduce the Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
R M Hafez - One of the best experts on this subject based on the ideXlab platform.
-
chebyshev collocation treatment of volterra Fredholm integral equation with error analysis
Arabian Journal of Mathematics, 2020Co-Authors: Y H Youssri, R M HafezAbstract:This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.
Fedor Sukochev - One of the best experts on this subject based on the ideXlab platform.
-
spectral flow is the integral of one forms on the banach manifold of self adjoint Fredholm operators
Advances in Mathematics, 2009Co-Authors: Alan L Carey, Denis Potapov, Fedor SukochevAbstract:Abstract One may trace the idea that spectral flow should be given as the integral of a one form back to the 1974 Vancouver ICM address of I.M. Singer. Our main theorem gives analytic formulae for the spectral flow along a norm differentiable path of self adjoint bounded Breuer–Fredholm operators in a semifinite von Neumann algebra. These formulae have a geometric interpretation which derives from the proof. Namely we define a family of Banach submanifolds of all bounded self adjoint Breuer–Fredholm operators and on each submanifold define global one forms whose integral on a norm differentiable path contained in the submanifold calculates the spectral flow along this path. We emphasise that our methods do not give a single globally defined one form on the self adjoint Breuer–Fredholms whose integral along all paths is spectral flow rather, as the choice of the plural ‘forms’ in the title suggests, we need a family of such one forms in order to confirm Singer's idea. The original context for this result concerned paths of unbounded self adjoint Fredholm operators. We therefore prove analogous formulae for spectral flow in the unbounded case as well. The proof is a synthesis of key contributions by previous authors, whom we acknowledge in detail in the introduction, combined with an additional important recent advance in the differential calculus of functions of non-commuting operators.
Kirtiwant P Ghadle - One of the best experts on this subject based on the ideXlab platform.
-
modified adomian decomposition method for solving fuzzy volterra Fredholm integral equation
Journal of the Indian Mathematical Society, 2018Co-Authors: Ahmed A Hamoud, Kirtiwant P GhadleAbstract:In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.
-
the reliable modified of laplace adomian decomposition method to solve nonlinear interval volterra Fredholm integral equations
The Korean Journal of Mathematics, 2017Co-Authors: Ahmed A Hamoud, Kirtiwant P GhadleAbstract:In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.
Ali Akbar Hoseini - One of the best experts on this subject based on the ideXlab platform.
-
numerical solution of nonlinear volterra Fredholm integral equations using hybrid of block pulse functions and taylor series
alexandria engineering journal, 2013Co-Authors: Farshid Mirzaee, Ali Akbar HoseiniAbstract:Abstract A numerical method based on an NM -set of general, hybrid of block-pulse function and Taylor series (HBT), is proposed to approximate the solution of nonlinear Volterra–Fredholm integral equations. The properties of HBT are first presented. Also, the operational matrix of integration together with Newton-Cotes nodes are utilized to reduce the computation of nonlinear Volterra–Fredholm integral equations into some algebraic equations. In addition, convergence analysis and numerical examples that illustrate the pertinent features of the method are presented.
