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NSDEBase.jl

This is the documentation of NSDEBase.jl, a Julia package containing common types and utility functions shared by NSDE.jl and its subpackages.

API

All exported types and functions are considered part of the public API, and thus documented in this manual.

NSDEBase.InitialValueProblem — Type
InitialValueProblem <: AbstractInitialValueProblem

A composite type for an initial-value problem.

Constructors

InitialValueProblem(rhs, u0, tspan)
InitialValueProblem(rhs, u0, t0, tN)
IVP(args...; kwargs...)

Arguments

  • rhs::AbstractRightHandSide : right-hand side function
  • u0::AbstractVector : initial condition
  • tspan::Tuple : end limits of time domain

Functions

  • copy : copy instance of problem with updated parameters
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NSDEBase.LinearRightHandSide — Type
LinearRightHandSide <: AbstractRightHandSide

A composite type for the right-hand side of an InitialValueProblem in the form $f(u, t) = L u + g(t)$.

Constructors

LinearRightHandSide(L, g, g!)
LinearRightHandSide(L[, g!_or_g])
LRHS(args...; kwargs...)

Arguments

  • L::AbstractMatrix : $L$, the coefficient term
  • g::Function : $g$, the forcing term, independent of $u$
  • g!::Function : $g$ but in-place
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NSDEBase.LinearRightHandSide — Method
(rhs::LinearRightHandSide)(u, t)
(rhs::LinearRightHandSide)(du, u, t)

returns the derivative du from the solution u and time t.

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NSDEBase.NonlinearRightHandSide — Type
NonlinearRightHandSide <: AbstractRightHandSide

A composite type for the right-hand side of an InitialValueProblem in the generic form $f(u, t)$.

Constructors

NonlinearRightHandSide(f, f!, Df, Df!)
NonlinearRightHandSide(f!_or_f, iscomplex=false)
RightHandSide(args...; kwargs...)
RHS(args...; kwargs...)

Arguments

  • f::Function : $f$, the right-hand side function
  • f!::Function : $f$ but in-place
  • Df::Function : $\mathcal{D}f$, the Jacobian of $f$ with respect to $u$
  • Df!::Function : $\mathcal{D}f$ but in-place
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NSDEBase.SplitRightHandSide — Type
SplitRightHandSide <: AbstractRightHandSide

A composite type for the right-hand side of an InitialValueProblem in the form $f(u, t) = f_\text{s}(u, t) + f_\text{ns}(u, t)$.

Constructors

SplitRightHandSide(fₛ, fₙₛ)
SRHS(args...; kwargs...)

Arguments

  • fₛ::Union{LinearRightHandSide,NonlinearRightHandSide} : $f_\text{s}$, the stiff part of the right-hand side function $f$
  • fₙₛ::NonlinearRightHandSide} : $f_\text{ns}$, the non-stiff part of the right-hand side function $f$
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NSDEBase.SplitRightHandSide — Method
(rhs::SplitRightHandSide)(u, t)
(rhs::SplitRightHandSide)(du, u, t)

returns the derivative du from the solution u and time t.

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Base.copy — Method
copy(problem, u0, tspan)::InitialValueProblem
copy(problem, u0, t0, tN)::InitialValueProblem

returns a copy of problem with the same rhs but different u0 and tspan.

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Base.show — Method
show(io::IO, object::AbstractObject)

prints the full description of an object and its contents to a stream io.

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Base.summary — Method
summary(io::IO, object::AbstractObject)

prints the short description of an object to a stream io.

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NSDEBase.DoublePendulum — Function
DoublePendulum(u0=[π/4, π/4, 0.0, 0.0], tspan=(0.0, 1.0); μ=1.0, λ=1.0)::InitialValueProblem
DoublePendulum(u0, t0, tN; kwargs...)::InitialValueProblem

returns an InitialValueProblem for the double pendulum problem.

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NSDEBase.IVP — Method
InitialValueProblem <: AbstractInitialValueProblem

A composite type for an initial-value problem.

Constructors

InitialValueProblem(rhs, u0, tspan)
InitialValueProblem(rhs, u0, t0, tN)
IVP(args...; kwargs...)

Arguments

  • rhs::AbstractRightHandSide : right-hand side function
  • u0::AbstractVector : initial condition
  • tspan::Tuple : end limits of time domain

Functions

  • copy : copy instance of problem with updated parameters
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NSDEBase.LRHS — Method
LinearRightHandSide <: AbstractRightHandSide

A composite type for the right-hand side of an InitialValueProblem in the form $f(u, t) = L u + g(t)$.

Constructors

LinearRightHandSide(L, g, g!)
LinearRightHandSide(L[, g!_or_g])
LRHS(args...; kwargs...)

Arguments

  • L::AbstractMatrix : $L$, the coefficient term
  • g::Function : $g$, the forcing term, independent of $u$
  • g!::Function : $g$ but in-place
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NSDEBase.Lorenz — Function
Lorenz(u0=[2.0, 3.0, -14.0], tspan=(0.0, 1.0); σ=10.0, β=8/3, ρ=28.0)::InitialValueProblem
Lorenz(u0, t0, tN; kwargs...)::InitialValueProblem

returns an InitialValueProblem for the Lorenz equations.

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NSDEBase.Lorenz96 — Function
Lorenz96(u0=[ones(39); 1.01], tspan=(0.0, 1.0); F=8.0)::InitialValueProblem
Lorenz96(u0, t0, tN; kwargs...)::InitialValueProblem

returns an InitialValueProblem for the Lorenz-96 equations.

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NSDEBase.RHS — Method
NonlinearRightHandSide <: AbstractRightHandSide

A composite type for the right-hand side of an InitialValueProblem in the generic form $f(u, t)$.

Constructors

NonlinearRightHandSide(f, f!, Df, Df!)
NonlinearRightHandSide(f!_or_f, iscomplex=false)
RightHandSide(args...; kwargs...)
RHS(args...; kwargs...)

Arguments

  • f::Function : $f$, the right-hand side function
  • f!::Function : $f$ but in-place
  • Df::Function : $\mathcal{D}f$, the Jacobian of $f$ with respect to $u$
  • Df!::Function : $\mathcal{D}f$ but in-place
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NSDEBase.RightHandSide — Method
NonlinearRightHandSide <: AbstractRightHandSide

A composite type for the right-hand side of an InitialValueProblem in the generic form $f(u, t)$.

Constructors

NonlinearRightHandSide(f, f!, Df, Df!)
NonlinearRightHandSide(f!_or_f, iscomplex=false)
RightHandSide(args...; kwargs...)
RHS(args...; kwargs...)

Arguments

  • f::Function : $f$, the right-hand side function
  • f!::Function : $f$ but in-place
  • Df::Function : $\mathcal{D}f$, the Jacobian of $f$ with respect to $u$
  • Df!::Function : $\mathcal{D}f$ but in-place
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NSDEBase.Rössler — Function
Rössler(u0=[2.0, 0.0, 0.0], tspan=(0.0, 1.0); α=0.2, β=0.2, γ=5.7)::InitialValueProblem
Rössler(u0, t0, tN; kwargs...)::InitialValueProblem

returns an InitialValueProblem for the Rössler equations.

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NSDEBase.SRHS — Method
SplitRightHandSide <: AbstractRightHandSide

A composite type for the right-hand side of an InitialValueProblem in the form $f(u, t) = f_\text{s}(u, t) + f_\text{ns}(u, t)$.

Constructors

SplitRightHandSide(fₛ, fₙₛ)
SRHS(args...; kwargs...)

Arguments

  • fₛ::Union{LinearRightHandSide,NonlinearRightHandSide} : $f_\text{s}$, the stiff part of the right-hand side function $f$
  • fₙₛ::NonlinearRightHandSide} : $f_\text{ns}$, the non-stiff part of the right-hand side function $f$
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NSDEBase.SimplePendulum — Function
SimplePendulum(u0=[π/4, 0.0], tspan=(0.0, 2π/3 * √9.81))::InitialValueProblem
SimplePendulum(u0, t0, tN; kwargs...)::InitialValueProblem

returns an InitialValueProblem for the simple pendulum problem.

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NSDEBase.VanDerPol — Function
VanDerPol(u0=[1.0, 0.0], tspan=(0.0, 1.0); μ=1.0)::InitialValueProblem
VanDerPol(u0, t0, tN; kwargs...)::InitialValueProblem

returns an InitialValueProblem for the Van der Pol equation (in first-order form).

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