PDEtools
splitsys
split sets of (algebraic or differential) equations into uncoupled subsets
Calling Sequence
Parameters
Description
Examples
splitsys(sys, funcs)
sys
-
set of algebraic or differential equations
funcs
set with the indeterminate functions
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](..).
withPDEtools:
sys≔k−2q2t+2q3t=−diffp3t,t,k2q2t−2q3t=−diffp2t,t,2kq1t=−diffp1t,t,p3tα=diffq2t,t,p2tα+p3tm3=diffq3t,t,p1tm1=diffq1t,t
sys≔k−2q2t+2q3t=−ⅆⅆtp3t,k2q2t−2q3t=−ⅆⅆtp2t,p1tm1=ⅆⅆtq1t,p3tα=ⅆⅆtq2t,2kq1t=−ⅆⅆtp1t,p2tα+p3tm3=ⅆⅆtq3t
funcs≔indetssys,Function
funcs≔p1t,p2t,p3t,q1t,q2t,q3t
The system of ODEs is split into two subsets.
splitsyssys,funcs
p1tm1=ⅆⅆtq1t,2kq1t=−ⅆⅆtp1t,k−2q2t+2q3t=−ⅆⅆtp3t,k2q2t−2q3t=−ⅆⅆtp2t,p3tα=ⅆⅆtq2t,p2tα+p3tm3=ⅆⅆtq3t
Split a mixed algebraic-differential system of equations.
sys≔x=rxcosφx,difffx,x=cosgx,diffgx,x=fx,yx=rxsinφx
sys≔x=rxcosφx,ⅆⅆxfx=cosgx,ⅆⅆxgx=fx,yx=rxsinφx
splitsyssys,f,g,φ,rx
x=rxcosφx,yx=rxsinφx,ⅆⅆxfx=cosgx,ⅆⅆxgx=fx
Split a system of PDEs.
PDE_sys≔diffgx,y,x2=gx,y−fx,y,difffx,y,x=gx,y+fx,y,diffhx,y,z,x=zkx,y
PDE_sys≔∂∂xgx,y2=gx,y−fx,y,∂∂xfx,y=gx,y+fx,y,∂∂xhx,y,z=zkx,y
splitsysPDE_sys,fx,y,gx,y,hx,y,z,kx,y
∂∂xhx,y,z=zkx,y,∂∂xgx,y2=gx,y−fx,y,∂∂xfx,y=gx,y+fx,y
See Also
DEtools
splitstrip
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