EnsembleSolution: Collection of all solutions of an EnsembleProblem.

GeometricSolution: Solution of a geometric differential equation

Contains all fields necessary to store the solution of a GeometricProblem.

Fields

• t: time steps
• s: NamedTuple of DataSeries for each solution component
• step: store every step'th time step (default: 1)
• nstore: number of time steps to store
• offset: offset of current time step

Constructors

GeometricSolution(problem; step=1)

The usual way to initialise a Solution is by passing a GeometricProblem, which can for example be an ODEProblem or PODEProblem. The optional parameter step determines the intervals for storing the solution, i.e., if store > 1 only every store'th solution is actually stored.

Abstract atomic or single-step solution.

Constructors:

SolutionStep(equation)
SolutionStep(solution)
SolutionStep(solution, integrator)

Automatically construct the appropriate atomic solution based on the given equation or solution type. If an integrator is provided as, the internal field of the atomic solution is constructed according to the internal state of the integrator as obtained from the function internal_variables.

Copy the initial conditions of a EquationProblem to the current state of an atomic solution.

Returns a NamedTuple with the solution of the current time step.

Returns a NamedTuple with the solution of the previous time step.

Solution step for a DAEProblem.

Parameters

• DT: data type
• TT: time step type
• AT: array type
• IT: internal variable types

Fields

• t: time of current time step
• t̄: time of previous time steps
• q: current solution of q
• λ: current solution of λ
• μ: current solution of μ
• q̄: previous solutions of q
• λ̄: previous solutions of λ
• μ̄: previous solution of μ
• v: vector field of q
• v̄: vector field of q̄
• u: projective vector field of q
• ū: projective vector field of q̄
• q̃: compensated summation error of q
• internal: internal variables of the integrator (e.g., internal stages of a Runge-Kutta methods or solver output)

Constructors

SolutionStepDAE(t::TT, q::AT, λ::AT, internal::IT=NamedTuple())

Solution step for an ODEProblem.

Parameters

• DT: data type
• TT: time step type
• AT: array type
• IT: internal variable types

Fields

• t: time of current time step
• t̄: time of previous time step
• q: current solution of q
• q̄: previous solution of q
• v: vector field of q
• v̄: vector field of q̄
• q̃: compensated summation error of q
• internal: internal variables of the integrator (e.g., internal stages of a Runge-Kutta methods or solver output)

Constructors

SolutionStepODE(t::TT, q::AT; nhistory=1, internal::IT=NamedTuple())

Solution step for a PDAEProblem.

Parameters

• DT: data type
• TT: time step type
• AT: array type
• IT: internal variable types

Fields

• t: time of current time step
• t̄: time of previous time steps
• q: current solution of q
• p: current solution of p
• λ: current solution of λ
• μ: current solution of μ
• q̄: previous solution of q
• p̄: previous solution of p
• λ̄: previous solution of λ
• μ̄: previous solution of μ
• v: vector field of q
• f: vector field of p
• v̄: vector field of q̄
• f̄: vector field of p̄
• u: projective vector field of q
• ū: projective vector field of q̄
• g: projective vector field of p
• ḡ: projective vector field of p̄
• q̃: compensated summation error of q
• p̃: compensated summation error of p
• internal: internal variables of the integrator (e.g., internal stages of a Runge-Kutta methods or solver output)

Constructors

SolutionStepPDAE(t::TT, q::AT, p::AT, λ::AT; nhistory=1, internal::IT=NamedTuple())

Solution step for a PODEProblem.

Parameters

• DT: data type
• TT: time step type
• AT: array type
• IT: internal variable types

Fields

• t: time of current time step
• t̄: time of previous time step
• q: current solution of q
• p: current solution of p
• q̄: previous solution of q
• p̄: previous solution of p
• v: vector field of q
• f: vector field of p
• v̄: vector field of q̄
• f̄: vector field of p̄
• q̃: compensated summation error of q
• p̃: compensated summation error of p
• internal: internal variables of the integrator (e.g., internal stages of a Runge-Kutta methods or solver output)

Constructors

SolutionStepPODE(t::TT, q::AT, p::AT; nhistory=1, internal::IT=NamedTuple())