A collocation spectral method for two-dimensional Sobolev equations

This article mainly studies a collocation spectral method for two-dimensional (2D) Sobolev equations. To this end, a collocation spectral model based on the Chebyshev polynomials for the 2D Sobolev equations is first established. And then, the existence, uniqueness, stability, and convergence of the collocation spectral numerical solutions are discussed. Finally, some numerical experiments are provided to verify the corrections of theoretical results. This implies that the collocation spectral model is very effective for solving the 2D Sobolev equations.