Based on a node group , the Newman type rational operator is constructed in paper. The convergence rate of approximation to class non-smooth functions discussed, which regarding X. Moreover, if based further subdivision nodes, . result this paper superior results equidistant Chebyshev nodes first kind and second kind.

The purpose of this paper is two-fold. First, we develop the Petrov-Galerkin method and the iterated Petrov-Galerkin method for a class of nonlinear Hammerstein equations. Alpert [1] established a class of wavelet basis and applied it to approximate solutions of the Fredholm second kind integral equations by the Galerkin method. He then demonstrated an advantage of a wavelet basis application t...

The focus of this paper is on the numerical solution of linear systems of Fredhlom integral equations of the second kind. For this purpose, the Chebyshev cardinal functions with Gauss-Lobatto points are used. By combination of properties of these functions and the effective Clenshaw-Curtis quadrature rule, an applicable numerical method for solving the mentioned systems is formulated. Some erro...

The Conjugate Gradient method (CG), the Minimal Residual method (MINRES), or more generally, the Generalized Minimal Residual method (GMRES) are widely used to solve a linear system Ax = b. The choice of a method depends on A’s symmetry property and/or definiteness), and MINRES is really just a special case of GMRES. This paper establishes error bounds on and sometimes exact expressions for res...

dynamically adaptive numerical methods have been developed to find solutions for differential equations. thesubject of wavelet has attracted the interest of many researchers, especially, in finding efficient solutions fordifferential equations. wavelets have the ability to show functions at different levels of resolution. in this paper, a numerical method is proposed for solving the second pain...

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...

This paper presents an improved approach where the wavelet functions are developed for particularly two-dimensional (2D) trusses. In the proposed scheme, a clear-cut formulation in a fluent manner has been derived to numerically solve the second-ordered differential equation of motion governing 2D trusses using two different types of basis functions including, complicated Chebyshev and simple H...