A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems

Authors:
N. Mai-Duy;R. I. Tanner
Affiliations:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia;School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, NSW 2006, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 9
Cited 6

On the coefficients of integrated expansions of ultraspherical polynomials

SIAM Journal on Numerical Analysis
A note on the satisfaction of the boundary conditions for Chebyshev collocation methods in rectangular domains

Journal of Scientific Computing
The pseudospectral method for solving differential eigenvalue problems

Journal of Computational Physics
Roundoff error in computing derivatives using the Chebyshev differentiation matrix

Journal of Computational Physics
Generation of Pseudospectral Differentiation Matrices I

SIAM Journal on Numerical Analysis
Spectral methods in MatLab

Spectral methods in MatLab
A MATLAB differentiation matrix suite

ACM Transactions on Mathematical Software (TOMS)
Spectral Differencing with a Twist

SIAM Journal on Scientific Computing
Multiquadric collocation method with integralformulation for boundary layer problems

Computers & Mathematics with Applications

A numerical comparison of Chebyshev methods for solving fourth order semilinear initial boundary value problems

Journal of Computational and Applied Mathematics
Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations

Journal of Computational Physics
Spectral Chebyshev Collocation for the Poisson and Biharmonic Equations

SIAM Journal on Scientific Computing
Solving boundary value problems, integral, and integro-differential equations using Gegenbauer integration matrices

Journal of Computational and Applied Mathematics
Optimal Gegenbauer quadrature over arbitrary integration nodes

Journal of Computational and Applied Mathematics
On the optimization of Gegenbauer operational matrix of integration

Advances in Computational Mathematics

Quantified Score

Hi-index	7.30

Visualization

Abstract

This paper reports a new spectral collocation method for numerically solving two-dimensional biharmonic boundary-value problems. The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows: (i) the imposition of the governing equation at the whole set of grid points including the boundary points and (ii) the straightforward implementation of multiple boundary conditions. The performance of the proposed method is investigated by considering several biharmonic problems of first and second kinds; more accurate results and higher convergence rates are achieved than with conventional differential methods.