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splitsys

  

split sets of (algebraic or differential) equations into uncoupled subsets

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

splitsys(sys, funcs)

Parameters

sys

-

set of algebraic or differential equations

funcs

-

set with the indeterminate functions

Description

• 

The splitsys function returns the received set of equations split, as much as possible, into subsets of equations mutually coupled, but not coupled with the equations of the other subsets. This splitting of the set may be useful for solving the system.

• 

This function is part of the PDEtools package, and so it can be used in the form splitsys(..) only after executing the command with(PDEtools). However, it can always be accessed through the long form of the command by using PDEtools[splitsys](..).

Examples

withPDEtools:

sysp1tm1=ⅆⅆtq1t,k2q2t+2q3t=ⅆⅆtp3t,k2q2t2q3t=ⅆⅆtp2t,2kq1t=ⅆⅆtp1t,p2tα+p3tm3=ⅆⅆtq3t,p3tα=ⅆⅆtq2t

sys:=k2q2t+2q3t=ⅆⅆtp3t,k2q2t2q3t=ⅆⅆtp2t,p1tm1=ⅆⅆtq1t,p3tα=ⅆⅆtq2t,2kq1t=ⅆⅆtp1t,p2tα+p3tm3=ⅆⅆtq3t

(1)

funcsindetssys,Function

funcs:=p1t,p2t,p3t,q1t,q2t,q3t

(2)

The system of ODEs is split into two subsets.

splitsyssys,funcs

p1tm1=ⅆⅆtq1t,2kq1t=ⅆⅆtp1t,k2q2t+2q3t=ⅆⅆtp3t,k2q2t2q3t=ⅆⅆtp2t,p3tα=ⅆⅆtq2t,p2tα+p3tm3=ⅆⅆtq3t

(3)

Split a mixed algebraic-differential system of equations.

sysx=rxcosφx,yx=rxsinφx,ⅆⅆxfx=cosgx,ⅆⅆxgx=fx

sys:=x=rxcosφx,ⅆⅆxfx=cosgx,ⅆⅆxgx=fx,yx=rxsinφx

(4)

splitsyssys,f,g,r,φx

x=rxcosφx,yx=rxsinφx,ⅆⅆxfx=cosgx,ⅆⅆxgx=fx

(5)

Split a system of PDEs.

PDE_sysxfx,y=gx,y+fx,y,xgx,y2=gx,yfx,y,xhx,y,z=zkx,y

PDE_sys:=xgx,y2=gx,yfx,y,xfx,y=gx,y+fx,y,xhx,y,z=zkx,y

(6)

splitsysPDE_sys,fx,y,gx,y,hx,y,z,kx,y

xhx,y,z=zkx,y,xgx,y2=gx,yfx,y,xfx,y=gx,y+fx,y

(7)

See Also

DEtools

PDEtools

splitstrip

 


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