Abstract The new rational a -polynomials are used to solve the Falkner-Skan equation. These polynomials equipped with an auxiliary parameter. approximated solution equation is obtained by unknown coefficients. To find coefficients and parameter contained in polynomials, collocation method Chebyshev-Gauss points used. numerical examples show efficiency of this method.

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...

This paper is concerned with superconvergence properties of the direct discontinuous Galerkin (DDG) method for one-dimensional linear convection-diffusion equations. We prove, under some suitable choice of numerical fluxes and initial discretization, a 2k-th and (k + 2) -th order superconvergence rate of the DDG approximation at nodes and Lobatto points, respectively, and a (k + 1) -th order of...

This paper focuses on increasing the accuracy of low-order four-node quadrilateral finite elements for the transient analysis of wave propagation. Modified integration rules, originally proposed for time-harmonic problems, provide the basis for the proposed technique. The modified integration rules shift the integration points to locations away from the conventional Gauss or Gauss-Lobatto integ...

We study the optimal general rate of convergence of the n-point quadrature rules of Gauss and Clenshaw–Curtis when applied to functions of limited regularity: if the Chebyshev coefficients decay at a rate O(n−s−1) for some s > 0, Clenshaw–Curtis and Gauss quadrature inherit exactly this rate. The proof (for Gauss, if 0 < s < 2, there is numerical evidence only) is based on work of Curtis, Johns...

Abstract. We consider a general class of systems of overdetermined differential-algebraic equations (ODAEs). We are particularly interested in extending the application of the symplectic Gauss methods to Hamiltonian and Lagrangian systems with holonomic constraints. For the numerical approximation to the solution to these ODAEs, we present specialized partitioned additive Runge– Kutta (SPARK) m...

Abstract: In this paper we resume some results concerned our work about least-squares approximation on GaussLobatto points. We present explicit formulas for discrete orthogonal polynomials and give the three-term recurrence relation to construct such polynomials. We also show that the normal matrix on this set of nodes can be factorized as the sum of two symmetric matrices: a full rank matrix w...