DChange - 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 : LHPDE : LieAlgebrasOfVectorFields/LHPDE/DChange

DChange

perform change of variables on a LHPDE object

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

DChange (tr, obj, indep = ivars, dep = dvars, rifReduce = r, options)

dchange (tr, obj, indep = ivars, dep = dvars, rifReduce = r, options)

Parameters

tr

-

set of equations corresponding to the transformation from the old variables on the left-hand side of the equations to the new variables on the right-hand side.

obj

-

a LHPDE object

ivars

-

(optional) a list of new independent variable names

dvars

-

(optional) a list of new dependent variables as functions or names

r

-

(optional) true or false

options

-

optional arguments that will be passed down to PDEtools[dchange] command

Description

• 

The DChange method performs change of variables tr in the LHPDE object obj.

• 

The method returns a new LHPDE object written with respect to new dependent and independent variables that are on the right hand side of tr.

• 

The new dependent and independent variables can also be fully specified via the optional arguments indep = ivars and dep = dvars.

• 

The returned LHPDE object can be rif-reduced if the option rifReduce = true is specified.

• 

The method name dchange is provided as alias.

• 

This DChange method is based on the existing Maple function PDEtools[dchange].

• 

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

Examples

withLieAlgebrasOfVectorFields:

Example 1:

SLHPDEdiffux,y,x+diffux,y,y=0

Sxux,y+yux,y=0,indep=x,y,dep=ux,y

(1)

DChangex=r+s,y=rs,ux,y=vr,s,S

rvr,s=0,indep=r,s,dep=vr,s

(2)

Example 2:

SLHPDEdiffux,x+axux=0,dep=ux

Sⅆⅆxux+axux=0,indep=x,dep=ux

(3)

DChangex=t,ux=diffvt,t,S,dep=vt

ⅆ2ⅆt2vt+atⅆⅆtvt=0,indep=t,dep=vt

(4)

By specifying rifReduce = true, a rif-reduced LHPDE object is returned.

SpDChangex=t,ux=diffvt,t,S,dep=vt,rifReduce=true

Spⅆ2ⅆt2vt=atⅆⅆtvt,indep=t,dep=vt

(5)

IsRifReducedSp

true

(6)

Example 3:

SLHPDE,dep=ux,y,vx,y

S,indep=x,y,dep=ux,y,vx,y

(7)

DChangex=s,y=t,ux,y=φs,t,S,dep=φs,t,vs,t,δs,t

,indep=s,t,dep=φs,t,vs,t,δs,t

(8)

Compatibility

• 

The DChange command was introduced in Maple 2020.

• 

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

See Also

LHPDE (Object overview)

LieAlgebrasOfVectorFields[LHPDE]

PDEtools[dchange]