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 H1$$ {H}^1 $$ 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.