A Chebyshev–Galerkin method for fourth order problems
I. Pop, and C. Gheorghiu. Approximation and Optimization: Proceedings of the International Conference on Approximation and Optimization (Romania), II, Cluj-Napoca, ICAOR, Transilvania Press, (1996)
We propose an efficient implementation of the Chebyshev-Galerkin spectral method for differential equations of the fourth order with Dirichlet boundary conditions. This discretization leads to banded matrices which, compared with other methods of the same type, are better conditioned. The efficiency of the method is illustrated on an eigenvalue model problem, where an improved convergence can be observed and the spurious eigenvalues are removed.