论文信息 - Continuation of Periodic Solutions in Parabolic Partial Differential Equations

Continuation of Periodic Solutions in Parabolic Partial Differential Equations

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.

[1] M. Kubicek,et al. DERPER—an algorithm for the continuation of periodic solutions in ordinary differential equations , 1984 .

[2] Grégoire Nicolis,et al. Self-Organization in nonequilibrium systems , 1977 .

[3] 山田道夫. M. Kubicek and M. Marek: Computational Methods in Bifurcation Theory and Dissipative Structures, Springer-Verlag, New York and Berlin, 1983, xii+244ページ, 24.5×16cm, DM108 (12,960円) (Springer Series in Computational Physics). , 1985 .