Efficient and generic algorithm for rigorous integration forward in time of dPDEs. I

DOI10.1007/s10915-013-9749-1zbMath1296.65138OpenAlexW2054872603WikidataQ59398689 ScholiaQ59398689MaRDI QIDQ461203

Jacek Cyranka

Publication date: 10 October 2014

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-013-9749-1

zbMATH Keywords

FFTfast Fourier transformautomatic differentiationinterval arithmeticrigorous numericsdissipative PDE

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Numerical methods for discrete and fast Fourier transforms (65T50) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Complexity and performance of numerical algorithms (65Y20) Algorithms with automatic result verification (65G20) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (11)

A general method for computer-assisted proofs of periodic solutions in delay differential problems ⋮ A construction of two different solutions to an elliptic system ⋮ Rigorous numerics for nonlinear heat equations in the complex plane of time ⋮ Connecting Orbits for Compact Infinite Dimensional Maps: Computer Assisted Proofs of Existence ⋮ Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits ⋮ Computer-Assisted Proof of Heteroclinic Connections in the One-Dimensional Ohta--Kawasaki Model ⋮ A rigorous implicit \(C^1\) Chebyshev integrator for delay equations ⋮ An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs ⋮ Fixed points of a destabilized Kuramoto-Sivashinsky equation ⋮ Automatic differentiation for Fourier series and the radii polynomial approach ⋮ Validated computations for connecting orbits in polynomial vector fields

Uses Software

• FADBAD++
• CAPD
• Taylor

Cites Work

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