detools::autoreduce
--
autoreduction of a system of differential equationsdetools::autoreduce
autoreduces a system of
differential equations, i.e. it tries to simplify the equations as much
as possible by entering each equation into all the other ones. The
ultimate goal is to achieve a triangular form.
detools::autoreduce(sys, indl, depl)
detools::autoreduce(dfs)
sys |
- | the differential equations: a list ofexpressions. |
indl |
- | the independent variables: a list of (indexed) identifiers. |
depl |
- | the dependent variables: a list of (indexed) identifiers. |
dfs |
- | the differential equations: a list of elements of a
domain in Cat::DifferentialFunction(DV) . |
an autoreduced list of differential equations; the equations are
represented either as expressions (first form of call) or as elements
of a domain in Cat::DifferentialFunction(DV)
(second form
of call).
Cat::DifferentialFunction(DV)
, i.e.
by using the second call of detools::autoreduce
. Otherwise
the default ranking is used which sorts first by the order of the
derivative and then reverse lexicographically.We want to simplify the two differential equations
3*diff(u(x,y),x,y)+diff(u(x,y),y)=0 and
diff(u(x,y),x)=0. Obviously, the second order term in the
first equation is a derivative of the second equation. Thus it is
eliminated by detools::autoreduce
.
>> detools::autoreduce([3*u([x, y]) + u([y]), u([x])], [x, y], [u])
[u([x]), u([y])]