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An Efficient Spline Collocation Method for a Nonlinear Fourth-Order Reaction Subdiffusion Equation

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Abstract

The nonlinear fourth-order reaction–subdiffusion equation whose solutions display a typical initial weak singularity is considered. A new analytical technique is introduced to analyze orthogonal spline collocation (OSC) method based on L1 scheme on graded mesh. By introducing a discrete convolution kernel and discrete fractional Grönwall inequality, convergence of the scheme is proved rigorously. This novel analytical technique can provide new insights in analyzing other time fractional fourth-order differential equations with weakly singular solutions.

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Acknowledgements

We thank the anonymous referees for their valuable comments and suggestions which helped us to improve the manuscript a lot. The authors wish to thank Professor Graeme Fairweather for stimulating discussions and for his constant encouragement and support.

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Authors and Affiliations

  1. School of Science, Hunan University of Technology, Zhuzhou, 412007, China

    Haixiang Zhang & Xuehua Yang

  2. Department of Mathematics, Hunan Normal University, Changsha, 410081, China

    Da Xu

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  1. Haixiang Zhang
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  2. Xuehua Yang
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Correspondence to Xuehua Yang.

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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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Zhang, H., Yang, X. & Xu, D. An Efficient Spline Collocation Method for a Nonlinear Fourth-Order Reaction Subdiffusion Equation. J Sci Comput 85, 7 (2020). https://doi.org/10.1007/s10915-020-01308-8

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  • DOI: https://doi.org/10.1007/s10915-020-01308-8

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