ParametricDerivatives - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Differential Equations : Lie Symmetry Method : Commands for PDEs (and ODEs) : LieAlgebrasOfVectorFields : LAVF : LieAlgebrasOfVectorFields/LAVF/ParametricDerivatives

ParametricDerivatives

 find the parametric derivatives of a LAVF object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

ParametricDerivatives( obj)

ParametricDerivatives( obj, order= m .. n)

ParametricDerivatives( obj, order= m)

Parameters

obj

-

a LAVF object

m, n

-

non-negative integers

Description

• 

The ParametricDerivatives method finds the parametric derivatives of a LAVF object. The parametric derivatives are returned as a list of functions.

• 

The method is front-end to the corresponding method of a LHPDE object. That is, let L be a LAVF object and S be its determining system as a LHPDE object (i.e. S = GetDeterminingSystem(L)), then the call ParametricDerivatives(L) is equivalent to ParametricDerivatives(S). All remaining input arguments will be passed down to its determining system S level. See the method ParametricDerivatives of a LHPDE object for more detail.

• 

This method is associated with the LAVF object. For more detail, see Overview of the LAVF object.

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressξx,y,ηx,y:

First, construct an indeterminate vector field and a determining system, then construct an LAVF object from them...

VVectorFieldξx,yDx+ηx,yDy,space=x,y

Vξx+ηy

(1)

E2LHPDEdiffξx,y,y,y=0,diffηx,y,x=diffξx,y,y,diffηx,y,y=0,diffξx,y,x=0,indep=x,y,dep=ξ,η

E2ξy,y=0,ηx=ξy,ηy=0,ξx=0,indep=x,y,dep=ξ,η

(2)

LLAVFV,E2

Lξx+ηy&whereξy,y=0,ξx=0,ηx=ξy,ηy=0

(3)

Now we can find the parametric derivatives of L...

ParametricDerivativesL

η,ξ,ξy

(4)

ParametricDerivativesL,order=0

ξ,η

(5)

Compatibility

• 

The ParametricDerivatives command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

LAVF (Object overview)

LieAlgebrasOfVectorFields[VectorField]

LieAlgebrasOfVectorFields[LHPDE]

LieAlgebrasOfVectorFields[LAVF]

ParametricDerivatives