4 papers
Computer-Assisted Proofs in Dynamical Systems: A Case Study of a Heteroclinic Orbit in the Shimizu--Morioka System
Olivier Hénot, Akitoshi Takayasu
The radii polynomial approach is an a posteriori validation method based on the contraction of a quasi-Newton operator. We apply this strategy to give a computer-assisted proof of…
Computer-assisted proofs for finding the monodromy of Picard-Fuchs differential equations for a family of K3 toric hypersurfaces
Toshimasa Ishige, Akitoshi Takayasu
In this paper, we present a numerical method for rigorously finding the monodromy of linear differential equations. Beginning at a base point where certain particular solutions are…
A rigorous integrator and global existence for higher-dimensional semilinear parabolic PDEs via semigroup theory
Gabriel William Duchesne, Jean-Philippe Lessard, Akitoshi Takayasu
In this paper, we introduce a general constructive method to compute solutions of initial value problems of semilinear parabolic partial differential equations on hyper-rectangular…
Validated matrix multiplication transform for orthogonal polynomials with applications to computer-assisted proofs for PDEs
Matthieu Cadiot, Jonathan Jaquette, Jean-Philippe Lessard +1
In this paper, we achieve three primary objectives related to the rigorous computational analysis of nonlinear PDEs posed on complex geometries such as disks and cylinders. First,…