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Analysis, Modelling, Optimization, and Numerical Techniques pp 139–150Cite as

Stability Analysis of a Finite Difference Scheme for a Nonlinear Time Fractional Convection Diffusion Equation

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 121))

Abstract

The nonlinear time fractional convection diffusion equation (TFCDE) is obtained from a standard nonlinear convection diffusion equation by replacing the first-order time derivative with a fractional derivative (in Caputo sense) of order \(\alpha \in (0,1)\). Developing numerical methods for solving fractional partial differential equations is of increasing interest in many areas of science and engineering. In this chapter, an explicit conservative finite difference scheme for TFCDE is introduced. We find its Courant–Friedrichs–Lewy (CFL) condition and prove encouraging results regarding stability, namely, monotonicity, the total variation diminishing (TVD) property and several bounds. Illustrative numerical examples are included in order to evaluate potential uses of the new method.

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Acknowledgment

CDA and CEM acknowledge support by Universidad Nacional de Colombia through the project Mathematics and Computation, Hermes code 20305. CDA and PAA acknowledge support by COLCIENCIAS through the project Programa jóvenes investigadores e innovadores 2012 (contrato 566), Hermes code 16243. CEM acknowledge support by Universidad Nacional de Colombia through the project Fortalecimiento del grupo de computación científica, Hermes code 16084.

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Authors and Affiliations

  1. Departamento de Matemáticas y Estadística, sede Manizales, Universidad Nacional de Colombia, Manizales, Colombia

    Carlos D. Acosta & Pedro A. Amador

  2. Escuela de Matemáticas, sede Medellín, Universidad Nacional de Colombia, Medellín, Colombia

    Carlos E. Mejía

Authors
  1. Carlos D. Acosta
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  2. Pedro A. Amador
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  3. Carlos E. Mejía
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Correspondence to Carlos D. Acosta .

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Editors and Affiliations

  1. Department of Electric, Electronic and Computer Science, Universidad Nacional de Colombia, Manizales, Colombia

    Gerard Olivar Tost

  2. Mathematics, Universidad del Valle, Cali, Colombia

    Olga Vasilieva

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Acosta, C., Amador, P., Mejía, C. (2015). Stability Analysis of a Finite Difference Scheme for a Nonlinear Time Fractional Convection Diffusion Equation. In: Tost, G., Vasilieva, O. (eds) Analysis, Modelling, Optimization, and Numerical Techniques. Springer Proceedings in Mathematics & Statistics, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-319-12583-1_10

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