# Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle

## Abstract

We are concerned with accurate Chebyshev collocation (ChC) solutions to fourth order eigenvalue problems. We consider the 1D case as well as the 2D case. In order to improve the accuracy of computation we use the precondtitioning strategy for second order differential operator introduced by Labrosse in 2009. The fourth order differential operator is factorized as a product of second order operators. In order to asses the accuracy of our method we calculate the so called drift of the first five eigenvalues. In both cases ChC method with the considered preconditioners provides accurate eigenpairs of interest.

## Authors

Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

## Keywords

spectral methods; Chebyshev collocation; preconditioning; fourth order eigenvalue problems;

## Paper coordinates

I. Boros, Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle, J. Numer. Anal. Approx. Theory, 46 (2017) no. 1, pp. 38-46.

## PDF

##### Journal

Journal of Numerical Analysis and Approximation Theory

2501-059X

2457-6794