A nonuniform linearized Galerkin-spectral method for nonlinear fractional pseudo-parabolic equations based on admissible regularities

In this paper, we deal with the nonlinear fractional pseudo-parabolic equations (FPPEs). We propose an accurate numerical algorithm for solving the aforementioned well-known equation. The problem is discretized in the temporal direction by utilizing a graded mesh linearized scheme and in the spatial direction by the Galerkin-spectral scheme. We investigate the stability conditions of the proposed scheme. We also provide an $H^1$ error estimate of the proposed approach to demonstrate that it is convergent with temporal second-order accuracy for fitted grading parameters. The proposed scheme is also extended to tackle coupled FPPEs. Numerical experiments are provided to validate the accuracy and reliability of the proposed scheme.