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Abstract
The modified anomalous sub-diffusion equation (MASDE) describes processes that become less anomalous as time progresses. In this paper, based on Crank-Nicolson and weighted and shifted Grünwald difference (WSGD) formula, we develop orthogonal spline collocation (OSC) method with second-order temporal accuracy and fourth-order spatial accuracy for MASDE. The stability and convergence of our numerical schemes are analysed in detail. Also, our numerical results are consistent with our theoretical analysis.
Acknowledgements
We thank the anonymous referees for their valuable comments and suggestions which helped us to improve the manuscript a lot.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
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).