Abstract
Fractional reaction–subdiffusion equations are widely used in recent years to simulate physical phenomena. In this paper, we consider a variable-order nonlinear reaction–subdiffusion equation. A numerical approximation method is proposed to solve the equation. Its convergence and stability are analyzed by Fourier analysis. By means of the technique for improving temporal accuracy, we also propose an improved numerical approximation. Finally, the effectiveness of the theoretical results is demonstrated by numerical examples.
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Chen, CM., Liu, F., Turner, I. et al. Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation. Numer Algor 63, 265–290 (2013). https://doi.org/10.1007/s11075-012-9622-6
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DOI: https://doi.org/10.1007/s11075-012-9622-6
Keywords
- Nonlinear reaction–subdiffusion equation
- Variable-order Riemann–Liouville partial derivative
- Improved numerical approximation
- Convergence and stability