[PDF] Top 20 Solving singular integral equations by using orthogonal polynomials

... second function of both variables) for some m ≥ 0, 0 < ν ≤ 1, and they are approximated by a finite Chebyshev series of order M . Moreover, for sufficiently large value of M, the homogeneous equation corresponding to ... See full document

... untz-logarithmic polynomials as well as the generalized Gauss quadrature method for the integrals with logarithmic weight ...method using M¨ untz-logarithmic polynomials to approximate the solution ... See full document

... multiple orthogonal polynomials, there is a rich bibliography [2–4, ...and integral representations of the linear forms £ 0 and £ 1 have been established ... See full document

... The purpose of this paper is to establish the Poincar´e-type inequalities for the composition of the homotopy operator T, differential operator d, and Green’s operator G under Lipschitz and BMO norms. One of the reasons ... See full document

... Chebyshev polynomials method of the first kindof degree n to solve linear Volterra weakly singular integro- differential equations (LVWSIDEs) of the second ...weakly singular integro- ... See full document

... for solving nonlinear Fredholm-Volterra integral equations, ...Bell polynomials. By using these matrices, nonlinear Fredholm-Volterra integral equations reduce to the ... See full document

... Volterra integral equations using Ga- lerkin ...terra integral equations of the first and second kind respectively using orthogonal polynomials as trial functions ... See full document

... the integral equation can be classified into two classes, which are Volterra integral equations and Fredholm integral ...Volterra integral equations are special type of ... See full document

... mixed integral equation of the first kind of type Fredholm- Volterra in position and time, ...Fredholm integral term is considered in a variable position, in the space L 2 [  1 , 1 ] , and has a ... See full document

... of solving a system of Maxwell equations in non-regular infinite ...hypersingular integral equations solved by specially developed numerical algorithms utilizing a singularity isolating ... See full document

... . Equations of this form are usually difficult to solve analytically so it is required to obtain an efficient approximate or numerical ...integro-differential equations has been proposed by collocation ... See full document

... Fredholm integral equations system to a set of algebraic ...obtained using the TFs is quite satis- factory in comparison with the other ...the integral equations system given in Example ... See full document

... of singular integral equations by using Chebyshev polyno- mials of first, second, third and fourth kind to obtain systems of linear algebraic equations, these systems are solved ...for ... See full document

... weakly singular kernels where the au- thors transform integral equation to linear differential equation ...Chebyshev polynomials, Leg- endre wavelets, Bernoulli series, Euler series, Legendre series ... See full document

... The aim of the present work is to introduce a method based on the Cheby- shev polynomials for numerical solution of a system of Cauchy type singular integral equations of the first kind on a ... See full document

... This section is devoted to computational results.We apply the presented method in this paper and solve several examples. Those examples are chosen whose exact solutions exist.All of the computations have been done ... See full document

... on solving the singular boundary integral equation with quadratic boundary elements of lagrangean ...the singular integrals. The singular boundary equation obtained with the direct ... See full document

... This paper is organized as follows: In the next section we review one-dimensional triangular functions. Section 3, presents stochastic concept that is used in this paper. Section 4, introduces stochastic integration ... See full document

... Using the finite Fourier transformation, the problem is converted to a singular integral equation that in turn can be reduced to an infinite system of algebraic equations.. The truncatio[r] ... See full document

... Madani in [] has compared the approximate solutions obtained by means of LHAM in a wide range of the problem’s domain with those results obtained from the exact analytical solutions and the HAM. This comparison shows a ... See full document