Error Analysis of Nonlinear Time Fractional Mobile/Immobile Advection-Diffusion Equation with Weakly Singular Solutions

In this paper, a weighted and shifted Grünwald-Letnikov difference (WSGD) Legendre spectral method is proposed to solve the two-dimensional nonlinear time fractional mobile/immobile advection-dispersion equation. We introduce correction deal with singularity in time, stability convergence analysis are proven. numerical implementation, fast applied based on globally uniform approximation of trapezoidal rule for integral real line decrease memory requirement computational cost. The cost O(Q) O(QK), respectively, where K number final step Q quadrature points used rule. Some experiments given confirm our theoretical effectiveness presented methods.