TMJets

The algorithm TMJets defaults to TMJets21b.

TMJets21a{N, DM<:AbstractDisjointnessMethod} <: AbstractContinuousPost

Validated integration using Taylor models with the validated_integ algorithm.

Fields

• orderQ – (optional, default: 2) order of the Taylor models for jet transport variables
• orderT – (optional, default: 8) order of the Taylor model in time
• abstol – (optional, default: 1e-10) absolute tolerance
• maxsteps – (optional, default: 2000) maximum number of steps in the validated integration $x' = f(x)$
• adaptive – (optional, default: true) if true, try decreasing the absolute tolerance each time step validation fails, until min_abs_tol is reached
• minabstol – (optional, default: 1e-29) minimum absolute tolerance for the adaptive algorithm
• disjointness – (optional, default: ZonotopeEnclosure()) defines the method to perform the disjointness check between the taylor model flowpipe and the invariant

Notes

The argument disjointness allows to control how are disjointness checks computed, in the case where the invariant is not universal. In particular, ZonotopeEnclosure() pre-processes the taylor model with a zonotopic overapproximation, then performs the disjointness check with that zonotope and the invariant. For other options, see the documentation of AbstractDisjointnessMethod.

This algorithm is an adaptation of the implementation in TaylorModels.jl (see copyright license in the file reach.jl of the current folder). The package TaylorIntegration.jl is used for jet-transport of ODEs using the Taylor method, and TaylorSeries.jl is used to work with truncated Taylor series.

TMJets21b{N, DM<:AbstractDisjointnessMethod} <: AbstractContinuousPost

Validated integration using Taylor models with the validated_integ2 algorithm.

Fields

• orderQ – (optional, default: 2) order of the Taylor models for jet transport variables
• orderT – (optional, default: 8) order of the Taylor model in time
• abstol – (optional, default: 1e-10) absolute tolerance
• maxsteps – (optional, default: 2000) maximum number of steps in the validated integration $x' = f(x)$
• adaptive – (optional, default: true) if true, try decreasing the absolute tolerance each time step validation fails, until min_abs_tol is reached
• minabstol – (optional, default: 1e-29) minimum absolute tolerance for the adaptive algorithm
• disjointness – (optional, default: ZonotopeEnclosure()) defines the method to perform the disjointness check between the taylor model flowpipe and the invariant

Notes

The argument disjointness allows to control how are disjointness checks computed, in the case where the invariant is not universal. In particular, ZonotopeEnclosure() pre-processes the taylor model with a zonotopic overapproximation, then performs the disjointness check with that zonotope and the invariant. For other options, see the documentation of AbstractDisjointnessMethod.

This algorithm is an adaptation of the implementation in TaylorModels.jl (see copyright license in the file reach.jl of the current folder). The package TaylorIntegration.jl is used for jet-transport of ODEs using the Taylor method, and TaylorSeries.jl is used to work with truncated Taylor series.