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Collocation-based numerical simulation of fractional order Allen–Cahn equation

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Abstract

This article looks for a reliable numerical technique to solve the Allen–Cahn equation using the Caputo time-fractional derivative. The fractional derivative semi-discretization approach using finite differences of the second order is shown first. The cubic B-spline collocation method is used to get a full discretization. We prove the conditional stability and convergence of the suggested approach. The technique’s effectiveness is demonstrated with numerical examples using two test problems. Numerical analysis confirms the approach’s efficiency and the method’s continued correctness.

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Authors and Affiliations

  1. Department of Mathematics, Birla Institute of Technology and Science, Pilani, Rajasthan, 333031, India

    Renu Choudhary & Devendra Kumar

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  1. Renu Choudhary
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  2. Devendra Kumar
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Renu Choudhary wrote the main manuscript text and carried out the numerical computations reported in the paper. Devendra Kumar gave the first draft of this work, and he has written the algorithm. He has also reviewed the manuscript.

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Correspondence to Renu Choudhary.

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Choudhary, R., Kumar, D. Collocation-based numerical simulation of fractional order Allen–Cahn equation. J Math Chem 62, 145–168 (2024). https://doi.org/10.1007/s10910-023-01525-0

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