Abstract
A numerical scheme comprising the Crank-Nicolson difference scheme in the temporal direction and cubic trigonometric <i>B</i>-spline method in the spatial direction is examined for the numerical solution of the variable coefficient time-fractional mobile-immobile solute transport equation. The time-fractional derivative is evaluated using the Atangana-Baleanu Caputo derivative. The equation has advection, dispersion, and reaction coefficients that can be influenced simultaneously by space and time variables. The present numerical scheme is unconditionally stable and second-order convergent in the temporal and spatial directions. Several test problems are solved to confirm the theoretical results.
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