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 Grünwald 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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Acknowledgements
Many thanks to Prof. Graeme Fairweather for stimulating discussions and for his constant encouragement and support.
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Communicated by Vasily E. Tarasov.
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The work was supported by National Natural Science Foundation of China (11701168, 11601144), Hunan Provincial Natural Science Foundation of China (2018JJ3108, 2018JJ3109, 2018JJ4062), Scientific Research Fund of Hunan Provincial Education Department (18B304, YB2016B033), and China Postdoctoral Science Foundation (2018M631403).
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Yang, X., Zhang, H. & Tang, Q. A spline collocation method for a fractional mobile–immobile equation with variable coefficients. Comp. Appl. Math. 39, 34 (2020). https://doi.org/10.1007/s40314-019-1013-3
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DOI: https://doi.org/10.1007/s40314-019-1013-3
Keywords
- Fractional convection diffusion equation
- Collocation method
- Variable coefficient
- Finite-difference method
- Stability and convergence