Accurate Spectral Collocation Computation of High Order Eigenvalues for Singular Schrödinger Equations

Accurate computation of singular values and eigenvalues of symmetric matrices ∗

We give the review of recent results in relative perturbation theory for eigenvalue and singular value problems and highly accurate algorithms which compute eigenvalues and singular values to the highest possible relative accuracy.

High-order Accurate Spectral Difference Method for Shallow Water Equations

ABSTRACT The conservative high-order accurate spectral difference method is presented for simulation of rotating shallowwater equations. The method is formulated using Lagrange interpolations on Gauss-Lobatto points for the desired order of accuracy without suffering numerical dissipation and dispersion errors. The optimal third-order total variation diminishing (TVD) Runge-Kutta algorithm is u...

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...

High-Order Collocation Methods for Differential Equations with Random Inputs

Recently there has been a growing interest in designing efficient methods for the solution of ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods. However, when the governing equations take complicated forms, numerical implementations of stochastic ...

Collocation for High-Order Differential Equations with Lidstone Boundary Conditions