Abstract
In this work we provide a numerical method for the diffusion equation with distributed order in time. The basic idea is to expand the unknown function in Chebyshev polynomials for the time variable t and reduce the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply the method to the forward and backward problems. Some numerical experiments are provided in order to show the performance and accuracy of the proposed method.
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Acknowledgements
This work was partially supported by FCT (Portuguese Foundation for Science and Technology) within the projects UID/MAT/00013/2013 (Centro de Matemática) and UID/MAT/00297/2013 (Centro de Matemática e Aplicações).
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Morgado, M.L., Rebelo, M. (2016). Chebyshev Spectral Approximation for Diffusion Equations with Distributed Order in Time. In: Pinelas, S., Došlá, Z., Došlý, O., Kloeden, P. (eds) Differential and Difference Equations with Applications. ICDDEA 2015. Springer Proceedings in Mathematics & Statistics, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-319-32857-7_24
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DOI: https://doi.org/10.1007/978-3-319-32857-7_24
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