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Legendre Collocation Spectral Method for Solving Space Fractional Nonlinear Fisher’s Equation

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Theory, Methodology, Tools and Applications for Modeling and Simulation of Complex Systems (AsiaSim 2016, SCS AutumnSim 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 643))

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Abstract

We consider the initial boundary value problem of the space fractional nonlinear Fisher’s equations on the general interval (a,b) and the fractional derivative is described in Caputo sense, the boundary conditions are nonhomogeneous. A fully discrete Legendre collocation spectral approximation scheme is structured basing Legendre-Gauss-Lobatto points in space and backward difference in time. We also use the operational matrix of the fractional derivative. Numerical experiments are presented with comparisons between Legendre collocation spectral method and other methods, and the results show that Legendre collocation spectral method is an alternative method for solving Fisher’s equation.

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Acknowledgements

This work is supported by the NSF of China (No. 11272024).

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Authors and Affiliations

  1. School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, China

    Zeting Liu, Shujuan Lv & Xiaocui Li

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  1. Zeting Liu
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  2. Shujuan Lv
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  3. Xiaocui Li
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Correspondence to Zeting Liu .

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Editors and Affiliations

  1. Beihang University, Beijing, China

    Lin Zhang

  2. Beihang University, Beijing, China

    Xiao Song

  3. Beihang University, Beijing, China

    Yunjie Wu

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Liu, Z., Lv, S., Li, X. (2016). Legendre Collocation Spectral Method for Solving Space Fractional Nonlinear Fisher’s Equation. In: Zhang, L., Song, X., Wu, Y. (eds) Theory, Methodology, Tools and Applications for Modeling and Simulation of Complex Systems. AsiaSim SCS AutumnSim 2016 2016. Communications in Computer and Information Science, vol 643. Springer, Singapore. https://doi.org/10.1007/978-981-10-2663-8_26

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  • DOI: https://doi.org/10.1007/978-981-10-2663-8_26

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2662-1

  • Online ISBN: 978-981-10-2663-8

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