Abstract Two efficient quadrature formulae have been developed for evaluating numerically certain singular integral equations of the first kind over the finite interval [-1,1]. Central to this work is the application of four special cases of the Jacobi polynomials P n (x), whose zeros served as interpolation and collocation nodes: (i) α = β = −2 , Tn(x), the first kind Chebyshev polynomials (ii...

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

In this paper, we propose the Chebyshev wavelet approximation for the numerical solution of a class of integrodifferential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. We show that the Chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. Illustrative examples are included to...

In this paper, the Chebyshev-I conformable differential equation is considered. A proper power series examined; there are two solutions, even solution and odd solution. The Rodrigues’ type formula also allocated for polynomials.

An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its sup...

A simple strategy for constructing a sequence of increasingly refined interpolation grids over the triangle or the tetrahedron is discussed with the goal of achieving uniform convergence and ensuring high interpolation accuracy. The interpolation nodes are generated based on a one-dimensional master grid comprised of the zeros of the Lobatto, Legendre, Chebyshev, and second-kind Chebyshev polyn...