Abstract
Numerical methods for construction of solution diagram of steady state and periodic solutions in ODE are well developed, e.g. [1,4]. Similarly, methods for study of parametric dependences of time independent (steady-state) solutions in PDE were also described, see e.g. [4]. However, no numerical algorithm for construction of a continuous dependence of periodic solutions of a system of PDEs of parabolic type on a parameter has appeared in literature until now. In this paper we shall describe two such methods and discuss the results of their application to a relatively simple system of two coupled nonlinear PDEs describing a common type of reaction-diffusion problem.
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References
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© 1987 Birkhäuser Verlag Basel
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Holodniok, M., Knedlík, P., Kubíček, M. (1987). Continuation of Periodic Solutions in Parabolic Partial Differential Equations. In: Küpper, T., Seydel, R., Troger, H. (eds) Bifurcation: Analysis, Algorithms, Applications. ISNM 79: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 79. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7241-6_13
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DOI: https://doi.org/10.1007/978-3-0348-7241-6_13
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