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LHSolve

attempts to solve a LHPDEs system of finite type.

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

LHSolve( obj, output = out, consts = c)

Parameters

obj

-

a LHPDE object that is of finite type (see IsFiniteType)

out

-

(optional) a string: either "solution", "basis", or "lhpde"

c

-

(optional) a name or a list of names

Description

• 

The LHSolve method attempts to solve the linear homogeneous PDEs in a LHPDE object.

• 

If solving is successful then the method returns a list of equations as the general solution.

• 

By specifying output = "basis", the returned output will be a list of lists of equations representing each solution in a basis.

• 

By specifying output = "lhpde", the returned output will be a new LHPDE object that is fully integrated.

• 

For a returned LHPDE object S that involves constants of integration variables, these variables are treated as additional dependent variables of S. The default names are _C1,_C2, ...

• 

The constant of integration variables can be renamed by specifying the optional argument consts = c.

– 

By specifying consts = alpha (i.e. a name), the constants of integration will be named as α1,α2,α3,

– 

By specifying consts = [alpha, beta, phi...](i.e. a list of names), the constants of integration will be named as α,β,φ,

• 

This is a front-end to the existing pdsolve command (for partial DEs system) and the dsolve command (for ordinary DEs system) of finite type.

• 

The method throws an exception if the LHPDEs system is not of finite type.

• 

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

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressα,β,η,ξx,y:

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

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

(1)

IsFiniteTypeS

true

(2)

LHSolveS

ξ=_C1y+_C3,η=_C1x+_C2

(3)

LHSolveS,consts=α,β,δ

ξ=αy+δ,η=αx+β

(4)

LHSolveS,output=basis

ξ=y,η=x,ξ=0,η=1,ξ=1,η=0

(5)

LHSolveS,output=lhpde,consts=α

ξ=yα1+α3,η=xα1+α2,indep=x,y,dep=ξ,η,α1,α2,α3

(6)

Compatibility

• 

The LHSolve 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]

IsFiniteType

pdsolve

dsolve