Abstract
In this work we explore the use of tempered fractional derivatives in the modelling of transient currents in disordered materials. We particularly focus on the numerical approximation of the involved problems. As it is known, the solutions of fractional differential equations usually exhibit singularities in the origin in time, and therefore, a decreasing of the convergence order of standard numerical schemes may be expected. In order to overcome this, we propose a finite difference scheme on a time graded mesh, in which the grading exponent can be properly chosen, taking into account the singularity type. Numerical results are presented and discussed.
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Acknowledgements
The authors acknowledge the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through projects UID/Multi/04621/2013 and PEst-OE/EEI/LA0008/2013, respectively.
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Morgado, M., Morgado, L.F. (2019). Modelling Time-of-Flight Transient Currents with Time-Fractional Diffusion Equations. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_17
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DOI: https://doi.org/10.1007/978-3-030-27550-1_17
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