In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...

The electrostatic interpretation of the Jacobi–Gauss quadrature points is exploited to obtain interpolation points suitable for approximation of smooth functions defined on a simplex. Moreover, several new estimates, based on extensive numerical studies, for approximation along the line using Jacobi–Gauss–Lobatto quadrature points as the nodal sets are presented. The electrostatic analogy is ex...

in this paper, an effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (rbfs). we present an algorithm based on interpolation by radial basis functions including multiquadratics (mqs), using legendre-gauss-lobatto nodes and weights. also a theorem is proved for convergence of the algorithm. some numerical examples are presented...

This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as points and derived differentiation matrices for derivatives. With matrices, were transformed into linear systems, which are easier solve. Two types of numerical simulations, results demo...

We describe a new spectral multidomain method for the solution of the compressible Navier-Stokes equations. Within each subdomain, the method collocates the solution unknowns and the gradients at the nodes of the Gauss-Chebyshev quadrature. The total fluxes are evaluated at the nodes of the Gauss-Lobatto quadrature. Both conforming and non-conforming subdomain grids are allowed. Two examples ar...

In this paper we present explicit formulas for discrete orthogonal polynomials over the so-called Gauss-Lobatto Chebyshev points. We also give the “three-term recurrence relation” to construct such polynomials. As a numerical application, we apply our formulas to the least-squares problem.

In this paper, we present a numerical method for solving Hallen’s integral equation based on radial basis functions (RBFs). This method will represent the solution of Hallen’s integral equation by interpolating the radial basis functions based on Legendre-Gauss-Lobatto(LGL) nodes and weights. The numerical results show that the proposed method for Hallen’s integral equation is very accurate and...

Consider a hermitian positive-definite linear functional F, and assume we have m distinct nodes fixed in advance anywhere on the real line. In this paper we then study the existence and construction of nth rational Gauss-Radau (m = 1) and Gauss-Lobatto (m = 2) quadrature formulas that approximate F{f}. These are quadrature formulas with n positive weights and with the n−m remaining nodes real a...

In this paper, a numerical method is proposed for solving optimal control problem of Volterra integral equations using radial basis functions (RBFs) for approximating unknown function. Actually, the method is based on interpolation by radial basis functions including multiquadrics (MQs), to determine the control vector and the corresponding state vector in linear dynamic system while minimizing...

On the line and its tensor products, Fekete points are known to be the Gauss–Lobatto quadrature points. But unlike high-order quadrature, Fekete points generalize to non-tensor-product domains such as the triangle. Thus Fekete points might serve as an alternative to the Gauss–Lobatto points for certain applications. In this work we present a new algorithm to compute Fekete points and give resul...