@article{Ngondiep2023, 
author = {Eric Ngondiep},
title = {An efficient two-level factored method for advection-dispersion problem with spatio-temporal coefficients and source terms},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {5},
pages = {11498-11520},
keywords = {two-dimensional advection-dispersion equation, spatio-temporal coefficients, Crank-Nicolson approach, a two-level factored Crank-Nicolson method, stability and convergence rate},
url = {https://www.sciopen.com/article/10.3934/math.2023582},
doi = {10.3934/math.2023582},
abstract = {A two-level factored implicit scheme is considered for solving a two-dimensional unsteady advection-dispersion equation with spatio-temporal coefficients and source terms subjected to suitable initial and boundary conditions. The approach reduces multi-dimensional problems into pieces of one-dimensional subproblems and then solves tridiagonal systems of linear equations. The computational cost of the algorithm becomes cheaper and makes the method more attractive. Furthermore, the two-level approach is unconditionally stable, temporal second-order accurate and spatial fourth-order convergent. The developed numerical scheme is faster and more efficient than a broad range of methods widely studied in the literature for the considered initial-boundary value problem. The stability of the proposed procedure is analyzed in the        L          ∞        (      t          0        ,      T          f        ;      L          2        )-norm whereas the convergence rate of the algorithm is numerically analyzed using the        L          2        (      t          0        ,      T          f        ;      L          2        )-norm. Numerical examples are provided to verify the theoretical result.}
}