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Rigorous Numerics for PDEs with Indefinite Tail: Existence of a Periodic Solution of the Boussinesq Equation with Time-dependent Forcing

100%
Czechowski A., Zgliczyński P.
Schedae Informaticae
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2015
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vol. 24
PL
We consider the Boussinesq PDE perturbed by a time-dependent forcing. Even though there is no smoothing effect for arbitrary smooth initial data, we are able to apply the method of self-consistent bounds to deduce the existence of smooth classical periodic solutions in the vicinity of 0. The proof is non-perturbative and relies on construction of periodic isolating segments in the Galerkin projections.
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Cr-Lohner algorithm

100%
Wilczak D., Zgliczyński P.
Schedae Informaticae
|
2011
|
vol. 20
PL
We present a Lohner type algorithm for the computation of rigorous bounds for the solutions of ordinary differential equations and its derivatives with respect to the initial conditions up to an arbitrary order.
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