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Power series solutions for the KPP equation

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Abstract

In this paper we solve the KPP equation by a non numerical method. To this end we find power series solutions where the coefficients are computed recursively. We also prove convergence of the series and illustrate the method by few examples.

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References

  1. Ablowitz, M.J., Zeppetella, A.: Explicit solutions of Fisher’s equation for a special wave speed. Bull. Math. Biol. 41, 835–840 (1979)

    MathSciNet  Google Scholar 

  2. Fife, P.C., McLeod, J.B.: The approach of solutions of nonlinear diffusion equations to travelling front solutions. Arch. Ration. Mech. Anal. 65(4), 335–361 (1977)

    Article  MathSciNet  Google Scholar 

  3. Kolmogoroff, A., Petrovskii, I., Piscounoff, N.: Etude de l’équation de la diffusion avec croissance de la quantité de matière et son application à un problème biologique. Mosc. Univ. Math. Bull. 1, 1–25 (1937)

    Google Scholar 

  4. McKean, H.P.: Application of Brownian motion to the equation of Kolmogorov–Petrovskii–Piskunov. Commun. Pure Appl. Math. 28, 323–331 (1975)

    MathSciNet  Google Scholar 

  5. Murray, J.D: Mathematical biology, II. Spatial models and biomedical applications. In: Murray, J.D. (ed.) Interdisciplinary Applied Mathematics, vol. 18, 3rd edn. Springer, Berlin Heidelberg New York (2003)

    Google Scholar 

  6. Sánchez-Garduño, F., Maini, P.K.: Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher–KPP equations. J. Math. Biol. 33(2), 163–192 (1994)

    Article  MathSciNet  Google Scholar 

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Correspondence to Amin Boumenir.

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Boumenir, A. Power series solutions for the KPP equation. Numer Algor 43, 177–187 (2006). https://doi.org/10.1007/s11075-006-9052-4

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  • DOI: https://doi.org/10.1007/s11075-006-9052-4

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