Spectral approximation of third-order problems
The author introduces a Chebyshev collocation method for the partial differential equation \(u_t = u_{xxx}\) on the set \((x, t) \in (-1, 1) \times (0, T]\). The boundary conditions are of a Dirichlet sort which ensure stability. A computational investigation suggests that collocation at the Gauss-Lobatto points produces a stable numerical method. The author also presents a finite-difference preconditioner to be used with implicit temporal discretizations.
scientific article; zbMATH DE number 1455177