Rigorous Numerics for Dissipative PDEs III. An effective algorithm for rigorous integration of dissipative PDEs
نویسنده
چکیده
We describe a Lohner-type algorithm for rigorous integration of dissipative PDEs. Using it for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions we give a computer assisted proof the existence of multiple periodic orbits.
منابع مشابه
Rigorous Numerics for Dissipative Partial Differential Equations II. Periodic Orbit for the Kuramoto-Sivashinsky PDE-A Computer-Assisted Proof
We present a method of self-consistent a-priori bounds, which allows to study rigorously dynamics of dissipative PDEs. As an application present a computer assisted proof of an existence of a periodic orbit for the Kuramoto-Sivashinsky equation ut = (u )x− uxx− νuxxxx, u(t, x) = u(t, x + 2π), u(t, x) = −u(t,−x),
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