A highly efficient spectral-Galerkin method based on tensor product for fourth-order Steklov equation with boundary eigenvalue

Abstract In this study, a highly efficient spectral-Galerkin method is posed for the fourth-order Steklov equation with boundary eigenvalue. By making use of the spectral theory of compact operators and the error formulas of projective operators, we first obtain the error estimates of approximative eigenvalues and eigenfunctions. Then we build a suitable set of basis functions included in H 0 1 ( Ω ) ∩ H 2 ( Ω ) $H^{1}_{0}(\Omega)\cap H^{2}(\Omega)$ and establish the matrix model for the discrete spectral-Galerkin scheme by adopting the tensor product. Finally, we use some numerical experiments to verify the correctness of the theoretical results.