Differential operators

DifferentialOps

Module defining types describing differential operators and compositions thereof.

AbstractDifferentialOp

Represents a general differential operator.

Derivative{n} <: AbstractDifferentialOp

Specifies the n-th derivative of a function.

DerivativeUnitRange{m, n} <: AbstractDifferentialOp

Specifies a range of derivatives.

Examples

Two ways of constructing derivative ranges:

julia> Derivative(2):Derivative(4)
Derivative(2:4)

julia> Derivative(2:4)
Derivative(2:4)

julia> Tuple(Derivative(2:4))
(D{2}, D{3}, D{4})

ScaledDerivative{n} <: AbstractDifferentialOp

n-th derivative of a function scaled by a constant coefficient.

DifferentialOpSum <: AbstractDifferentialOp

Sum of two differential operators.

max_order(op::AbstractDifferentialOp)
max_order(ops...)

Get maximum derivative order of one or more differential operators.

AbstractNormalDirection

Represents the normal direction on a given domain boundary.

LeftNormal <: AbstractNormalDirection

Specifies the normal direction on the left boundary of a 1D domain.

The left normal direction goes opposite to the coordinate axis.

RightNormal <: AbstractNormalDirection

Specifies the normal direction on the right boundary of a 1D domain.

The right normal direction is equal to that of the coordinate axis.

dot(op::AbstractDifferentialOp, dir::AbstractNormalDirection) -> AbstractDifferentialOp

Project derivative along a normal direction.

This should be used to convert from a normal derivative at the boundaries, to a derivative along the coordinate axes of the domain.

In practice, this returns op for RightNormal. For LeftNormal, it multiplies the odd-order derivatives by -1.