Nodal point sets, and associated collocation projections, play an important role in a range of high-order methods, including Flux Reconstruction (FR) schemes. Historically, efforts have focused on identifying nodal sets that aim to minimise the L∞ error interpolating polynomial. The present work combines comprehensive review known approximation theory results, with new numerical experiments, mo...

We compute point sets on the triangle that have low Lebesgue constant, with sixfold symmetries and Gauss-Legendre-Lobatto distribution on the sides, up to interpolation degree 18. Such points have the best Lebesgue constants among the families of symmetric points used so far in the framework of triangular spectral elements.

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...

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration ordinary differential equations (ODEs) is presented. Its derivation based on integral form equation. The approach enables enhancing accuracy established Runge–Kutta while retaining same number stages. We demonstrate that, with proposed approach, Gauss–Legendre and Lobatto IIIA can be derived that th...

This is to certify that I have examined a copy of a technical report by Kazh Brito and found it satisfactory in all respects, and that any and all revisions required by the examining committee have been made. Abstract This is an exploration of Legendre spectral finite-element (LSFE) formulations for Reissner-Mindlin plates. The goal was to compare high-order LSFEs with standard low-order finite...

In this paper, we mainly study the superconvergence properties in approximation of second- and third-order BVPs by spectral collocation methods. The theoretical analyses identify points interpolation function. Ample numerical experiments are carried out which perfectly match results. addition, results show that also hold solving PDEs.

Recently, the Legendre pseudospectral (PS) method migrated from theory to flight application onboard the International Space Station for performing a finite-horizon, zeropropellant maneuver. A small technical modification to the Legendre PS method is necessary to manage the limiting conditions at infinity for infinite-horizon optimal control problems. Motivated by these technicalities, the conc...

This paper gives an ecient numerical method for solving the nonlinear systemof Volterra-Fredholm integral equations. A Legendre-spectral method based onthe Legendre integration Gauss points and Lagrange interpolation is proposedto convert the nonlinear integral equations to a nonlinear system of equationswhere the solution leads to the values of unknown functions at collocationpoints.