Shifted Legendre reproducing kernel Galerkin method for the quasilinear degenerate parabolic problem

This paper focuses on solving a class of quasilinear degenerate parabolic problems by using shifted Legendre reproducing kernel Galerkin method (SLRKGM for short). The quasilinear term was linearized and the time derivative was discretized by using the finite difference scheme. The basis functions were constructed by the shifted Legendre polynomials and the approximate solution was obtained by the Galerkin method. We also discussed the error estimates and stability analysis of the method. Numerical examples demonstrate the feasibility and reliability of our algorithm.