@article{Ngondiep2025, 
author = {Eric Ngondiep and Areej A. Binsultan and Ibtisam M. Aldawish},
title = {A two-stage fourth-order modified explicit Euler/Crank-Nicolson approach for a time-variable fractional transport model},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {8},
pages = {18123-18155},
keywords = {time-variable fractional transport model, explicit Euler scheme, Crank-Nicolson method, two-stage fourth-order modified explicit Euler/Crank-Nicolson approach, stability analysis, convergence rate},
url = {https://www.sciopen.com/article/10.3934/math.2025808},
doi = {10.3934/math.2025808},
abstract = {This paper considered a two-stage fourth-order modified explicit Euler/Crank-Nicolson numerical method for solving a time-variable fractional transport equation subject to suitable initial and boundary conditions. Both stability and error estimates of the new approach were deeply analyzed in the        L          ∞        (  0  ,  T  ;      L          2        )-norm. The analysis suggests that the proposed technique is unconditionally stable and converges with order    O  (  max  {      k          2      −              β        ¯              ,      k                  3        2              }  +      h          4        ), where        β    ¯   is a positive constant satisfying    0  <      β    ¯    <  1,    h and    k are the space step and time step, respectively. This result indicates that the two-stage fourth-order formulation is fast and efficient. Numerical experiments were performed to verify the unconditional stability and convergence rate of the developed algorithm.}
}