Differential-spectral approximation based on reduced-dimension scheme for fourth-order parabolic equation

We propose in this paper an efficient differential-spectral approximation based on a reduced-dimension scheme for a fourth-order parabolic equation in a circular domain. First, we decompose the original problem into a series of equivalent one-dimensional fourth-order parabolic problems, based on which a fully discrete scheme based on differential-spectral approximation is established, and its stability and corresponding error estimation are also proved. Then, we utilized the orthogonality of Legendre polynomials to construct a set of effective basis functions and derived the matrix form associated with the full discrete scheme. Finally, several numerical examples are performed, and the numerical results account for the effectiveness and high accuracy of our algorithm.