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Modelling Time-of-Flight Transient Currents with Time-Fractional Diffusion Equations

  • M. Luísa MorgadoEmail author
  • Luís F. Morgado
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)

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.

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Center for Computational and Stochastic Mathematics (CEMAT), Lisbon and Departamento de MatemáticaUniversidade de Trás-os-Montes e Alto Douro, UTADVila RealPortugal
  2. 2.Instituto de Telecomunicações, Lisboa, and Departamento de FísicaUniversidade de Trás-os-Montes e Alto Douro, UTADVila RealPortugal

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