On the equivalence between basis recombination and boundary bordering formulations for spectral collocation methods in rectangular domains

Abstract

The application of spectral collocation methods to second- and fourth-order boundary value problems in rectangular domains leads to systems of n algebraic equations in n unknowns. Under certain conditions, it may be shown that the systems obtained when imposing the boundary conditions in the boundary bordering sense and when satisfying them using a basis recombination formulation are equivalent. © 1993.