We introduce a radial basis collocation method to solve axially moving beam problems

In this paper we introduce a measure for calculating statistically significant collocation sets that is related to the Poisson distribution. We show that results calculated using this measure are comparable to well-known measures like the log-likelihood measure. Additionally, we discuss asymptotic behaviour and additivity as general properties of the measure which may be applied to the analysis...

In this work, the convection-diffusion integro-differential equation with a weakly singular kernel is discussed. The  Legendre spectral tau method is introduced for finding the unknown function. The proposed method is based on expanding the approximate solution as the elements of a shifted Legendre polynomials. We reduce the problem to a set of algebraic equations by using operational matrices....

in the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. for this purpose, we replace the problem with an alternative optimal control problem in which the switching t...

Abstract— A new polynomial method to solve Volterra–Fredholm Integral equations is presented in this work. The method is based upon Shifted Legendre Polynomials. The properties of Shifted Legendre Polynomials and together with Gaussian integration formula are presented and are utilized to reduce the computation of Volterra–Fredholm Integral equations to a system of algebraic equations. Some num...

In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [14] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also disc...