...Jalil Rashidinia; Zahra Mahmoodi Purpose The purpose of this paper is to develop a numerical method based on quintic B‐spline to solve the linear and nonlinear Fredholm and Volterra integral equations. Design/methodology/approach The solution is collocated by quintic B‐spline...

...Kazem Nouri Purpose The purpose of this paper is to discuss a numerical method for solving system of Volterra integral equations. Design/methodology/approach An expansion method known as Chebyshev collocation method is chosen to convert the system of integral equations to the linear algebraic...

...K. Maleknejad; M. Alizadeh; R. Mollapourasl Purpose The purpose of this paper is to discuss a numerical method for solving Fredholm integral equations of the first kind with degenerate kernels and convergence of this numerical method. Design/methodology/approach By using sinc collocation...

...Mohsen Rabbani; Khosrow Maleknejad Purpose The purpose of this paper is to explain the choice of Alpert multi‐wavelet as basis functions to discrete Fredholm integral equation of the second kind by using Petrov‐Galerkin method. Design/methodology/approach In this process, two kinds of matrices...

...Gaspar Mora; Lazhar Bougoffa; Manal Al‐Haqbani; Randolph C. Rach Purpose In this paper, Fredholm integral equations of the first kind, the Schlomilch integral equation, and a class of related integral equations of the first kind with constant limits of integration are transformed in such a manner...

... at the point 0. The theoretical contribution of the paper consists of establishing the characteristic function ϕ_Y(u) in equation (3) as the unique solution of an integral equation for characteristic functions, based on the transformation in equation (2) and the integral...

...Rahman Farnoosh; Ebrahimi Morteza Purpose The purpose of this paper is to provide a Monte Carlo variance reduction method based on Control variates to solve Fredholm integral equations of the second kind. Design/methodology/approach A numerical algorithm consisted of the combined use...

...Yves Cherruault; Feyed Ben Zitoun; Yves Cherruault Purpose The purpose of this paper is to present a method for solving nonlinear integral equations of the second and third kind. Design/methodology/approach The method converts the nonlinear integral equation into a system of nonlinear...

...Yves Cherruault; Ngarkodje Ngarasta Purpose The purpose of this paper is to find methods for solving linear or non‐linear integral equations. The decomposition method may be applied, but a difficulty arises when it is applied to integral equations of the first kind which are not in canonical form...

...Mian‐yun Chen; Yi Lin; Hejing Xiong; Ngarkodje Ngarasta; Koina Rodoumta; Henri Sosso Purpose The purpose of this paper is to solve systems of linear Volterra integral equations of the first kind by the Adomian decomposition method (ADM). An elegant and reliable technique is outlined to find...

...Mian‐yun Chen; Yi Lin; Hejing Xiong; Mohsen Rabbani; Khosrow Maleknejad Purpose The purpose of this paper is to use Alpert wavelet basis and modify the integrand function approximation coefficients to solve Fredholm‐Hammerstein integral equations. Design/methodology/approach...

...Elçin Yusufoğlu; Barış Erbaş Purpose This paper sets out to introduce a numerical method to obtain solutions of Fredholm‐Volterra type linear integral equations. Design/methodology/approach The flow of the paper uses well‐known formulations, which are referenced at the end, and tries...

...K. Maleknejad; H. Mesgarani Purpose Aims to present a boundary integral equation method for solving Laplace's equation Δu=0 with nonlinear boundary conditions. Design/methodology/approach The nonlinear boundary value problem is reformulated as a nonlinear boundary integral equation...

... to estimate the simple integral. Finally, we adapt the Filon's method, consisting in evaluating the Fourier coefficients of a function, to the oscillatory integrand obtained by using reducing transformations. © Emerald Group Publishing Limited 2004 Cybernetics Integral equations Numerical...

...K. Maleknejad; M. Tavassoli Kajani; Y. Mahmoudi Uses the continuous Legendre wavelets on the interval [0,1) in the manner of M. Razzaghi and S. Yousefi, to solve the linear second kind integral equations. We use quadrature formula for the calculation of inner products of any functions, which...

...]×[0,2π], we have proved that: Equation 1 where Argθ=θ−2kπ if θ∈[2kπ, 2(k+1)π] (k∈N). © MCB UP Limited 2003 Cybernetics Integral equations Numerical analysis First we give an approximation of a multiple integral...

... as α_i1…in on the chosen quadrature formula. © MCB UP Limited 2002 Integral equations Methods First recall the following Another approach is developed in a paper to appear. It consists of the approach f(x₁...

...Yves Cherruault; Virginie Seng Aims to solve Fredholm and Volterra non‐linear integral equations of the first kind. Uses the Adomian method, but since these equations are not under the canonical form u‐Nu = f, proposes some transformations for reducing the integral equations to integral...