OrdinaryDiffEqExtrapolation

ImplicitEulerExtrapolation(;
        autodiff = AutoForwardDiff(), concrete_jac = nothing,
        linsolve = nothing, max_order = 12, min_order = 3, init_order = 5,
        threading = false, sequence = :harmonic
    ) -> ImplicitEulerExtrapolation

Adaptive implicit Euler extrapolation, similar to SEULEX. It is intended for stiff problems and varies both its step size and extrapolation order.

Keywords

• autodiff = AutoForwardDiff(): ADTypes backend used to construct Jacobians.
• concrete_jac = nothing: Jacobian materialization policy. nothing lets the solver choose; use true or false to request or disable a concrete Jacobian.
• linsolve = nothing: LinearSolve algorithm for implicit stage systems. nothing selects the OrdinaryDiffEq default.
• max_order::Integer = 12: largest internal extrapolation order.
• min_order::Integer = 3: smallest internal extrapolation order; values below 3 are raised to 3.
• init_order::Integer = 5: initial internal order. It is raised when necessary so that min_order < init_order < max_order.
• threading = false: enable concurrent extrapolation columns when true.
• sequence::Symbol = :harmonic: subdivision sequence. Supported values are :harmonic, :romberg, and :bulirsch; other values warn and use :harmonic.

Returns

• ImplicitEulerExtrapolation: configured implicit extrapolation algorithm for CommonSolve.solve.

Examples

using OrdinaryDiffEqExtrapolation: ImplicitEulerExtrapolation
using CommonSolve: solve
using SciMLBase: ODEProblem

prob = ODEProblem((u, p, t) -> -100u, 1.0, (0.0, 1.0))
sol = solve(prob, ImplicitEulerExtrapolation(); abstol = 1.0e-10, reltol = 1.0e-8)

References

C. Elrod et al., "Parallelizing explicit and implicit extrapolation methods for ordinary differential equations," HPEC 2022, pp. 1-9.

ImplicitDeuflhardExtrapolation(;
        autodiff = AutoForwardDiff(),
        concrete_jac = nothing, linsolve = nothing, min_order = 1,
        init_order = 5, max_order = 10, sequence = :harmonic,
        threading = false
    ) -> ImplicitDeuflhardExtrapolation

Adaptive implicit midpoint extrapolation with Deuflhard's order and step-size selection. It targets stiff problems and uses barycentric extrapolation of the implicit midpoint approximations.

Keywords

• autodiff = AutoForwardDiff(): ADTypes backend used to construct Jacobians.
• concrete_jac = nothing: Jacobian materialization policy. nothing lets the solver choose; use true or false to request or disable a concrete Jacobian.
• linsolve = nothing: LinearSolve algorithm for implicit stage systems. nothing selects the OrdinaryDiffEq default.
• min_order::Integer = 1: smallest internal extrapolation order; values below 1 are raised to 1.
• init_order::Integer = 5: initial internal order. It is raised to at least min_order.
• max_order::Integer = 10: largest internal order. It is raised to at least init_order.
• sequence::Symbol = :harmonic: subdivision sequence. Supported values are :harmonic, :romberg, and :bulirsch; other values warn and use :harmonic.
• threading = false: enable concurrent extrapolation columns when true.

Returns

• ImplicitDeuflhardExtrapolation: configured implicit extrapolation algorithm for CommonSolve.solve.

Examples

using OrdinaryDiffEqExtrapolation: ImplicitDeuflhardExtrapolation
using CommonSolve: solve
using SciMLBase: ODEProblem

prob = ODEProblem((u, p, t) -> -100u, 1.0, (0.0, 1.0))
alg = ImplicitDeuflhardExtrapolation(sequence = :romberg)
sol = solve(prob, alg; abstol = 1.0e-10, reltol = 1.0e-8)

References

C. Elrod et al., "Parallelizing explicit and implicit extrapolation methods for ordinary differential equations," HPEC 2022, pp. 1-9.

ImplicitHairerWannerExtrapolation(;
        autodiff = AutoForwardDiff(),
        concrete_jac = nothing, linsolve = nothing, min_order = 2,
        init_order = 5, max_order = 10, sequence = :harmonic,
        threading = false
    ) -> ImplicitHairerWannerExtrapolation

Adaptive implicit midpoint extrapolation with the order and step-size controller from Hairer and Wanner's SODEX algorithm. It is intended for stiff problems and supports parallel evaluation of independent extrapolation columns.

Keywords

• autodiff = AutoForwardDiff(): ADTypes backend used to construct Jacobians.
• concrete_jac = nothing: Jacobian materialization policy. nothing lets the solver choose; use true or false to request or disable a concrete Jacobian.
• linsolve = nothing: LinearSolve algorithm for implicit stage systems. nothing selects the OrdinaryDiffEq default.
• min_order::Integer = 2: smallest internal extrapolation order; values below 2 are raised to 2.
• init_order::Integer = 5: initial internal order. It is raised when necessary so that min_order < init_order.
• max_order::Integer = 10: largest internal order. It is raised when necessary so that init_order < max_order.
• sequence::Symbol = :harmonic: subdivision sequence. Supported values are :harmonic, :romberg, and :bulirsch; other values warn and use :harmonic.
• threading = false: enable concurrent extrapolation columns when true.

Returns

• ImplicitHairerWannerExtrapolation: configured implicit extrapolation algorithm for CommonSolve.solve.

Examples

using OrdinaryDiffEqExtrapolation: ImplicitHairerWannerExtrapolation
using CommonSolve: solve
using SciMLBase: ODEProblem

prob = ODEProblem((u, p, t) -> -100u, 1.0, (0.0, 1.0))
alg = ImplicitHairerWannerExtrapolation(sequence = :bulirsch)
sol = solve(prob, alg; abstol = 1.0e-10, reltol = 1.0e-8)

References

C. Elrod et al., "Parallelizing explicit and implicit extrapolation methods for ordinary differential equations," HPEC 2022, pp. 1-9.

ImplicitEulerBarycentricExtrapolation(;
        autodiff = AutoForwardDiff(),
        concrete_jac = nothing, linsolve = nothing, min_order = 3,
        init_order = 5, max_order = 12, sequence = :harmonic,
        threading = false, sequence_factor = 2
    ) -> ImplicitEulerBarycentricExtrapolation

Adaptive implicit Euler extrapolation using barycentric coordinates and the Hairer-Wanner order and step-size strategy. It targets stiff problems and can evaluate independent extrapolation columns concurrently.

Keywords

• autodiff = AutoForwardDiff(): ADTypes backend used to construct Jacobians.
• concrete_jac = nothing: Jacobian materialization policy. nothing lets the solver choose; use true or false to request or disable a concrete Jacobian.
• linsolve = nothing: LinearSolve algorithm for implicit stage systems. nothing selects the OrdinaryDiffEq default.
• min_order::Integer = 3: smallest internal extrapolation order; values below 3 are raised to 3.
• init_order::Integer = 5: initial internal order. It is raised when necessary so that min_order < init_order.
• max_order::Integer = 12: largest internal order. It is raised when necessary so that init_order < max_order.
• sequence::Symbol = :harmonic: subdivision sequence. Supported values are :harmonic, :romberg, and :bulirsch; other values warn and use :harmonic.
• threading = false: enable concurrent extrapolation columns when true.
• sequence_factor::Integer = 2: positive multiplier applied to the subdivision sequence used by the implicit Euler base method.

Returns

• ImplicitEulerBarycentricExtrapolation: configured implicit extrapolation algorithm for CommonSolve.solve.

Examples

using OrdinaryDiffEqExtrapolation: ImplicitEulerBarycentricExtrapolation
using CommonSolve: solve
using SciMLBase: ODEProblem

prob = ODEProblem((u, p, t) -> -100u, 1.0, (0.0, 1.0))
alg = ImplicitEulerBarycentricExtrapolation(sequence = :romberg)
sol = solve(prob, alg; abstol = 1.0e-10, reltol = 1.0e-8)

References

C. Elrod et al., "Parallelizing explicit and implicit extrapolation methods for ordinary differential equations," HPEC 2022, pp. 1-9.