Computer assisted Fourier analysis in sequence spaces of varying regularity. This work treats a functional analytic framework for computer assisted Fourier analysis which can be used to obtain mathematically rigorous error bounds on numerical approximations of solutions of differential equations. An abstract a posteriori theorem is employed in order to obtain existence and regularity results for C k problems with 0<k≤∞ or k=ω. The main tools are certain infinite sequence spaces of rapidly decaying coefficients: we employ sequence spaces of algebraic and exponential decay rates in order to characterize the regularity of our results. We illustrate the implementation and effectiveness of the method in a variety of regularity classes. We also examine the effectiveness of spaces of algebraic decays for studying solutions of problems near the breakdown of analyticity.
Keywords for this software
References in zbMATH (referenced in 6 articles )
Showing results 1 to 6 of 6.
- Alama, Yvonne Bronsard; Lessard, Jean-Philippe: Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption (2020)
- Jaquette, Jonathan: A proof of Jones’ conjecture (2019)
- Reinhardt, Christian; Mireles James, J. D.: Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation (2019)
- Breden, Maxime; Lessard, Jean-Philippe: Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs (2018)
- Lessard, Jean-Philippe; Mireles James, J. D.: Computer assisted Fourier analysis in sequence spaces of varying regularity (2017)
- Lessard, Jean-Philippe; Sander, Evelyn; Wanner, Thomas: Rigorous continuation of bifurcation points in the diblock copolymer equation (2017)