Abstract
The Crank–Nicolson orthogonal spline collocation (OSC) methods are considered for approximate solution of the variable coefficient fractional mobile–immobile equation. The convection, diffusion, and reaction coefficients can depend on both the spatial and temporal variables, simultaneously. Combining with Crank–Nicolson scheme and weighted and shifted Grunwald difference approximation in time, we establish OSC method in space. It is proved that our proposed fully methods are of optimal order in certain $$H_j$$ ($$j=0,1$$) norms. Moreover, we derive $$L^{\infty }$$ estimates in space. Numerical results are also provided to verify our proposed algorithm.
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