questions on ODE



Dear Community,

I'm facing some questions on ODE.

1. Is there an analytical solution to an ode with a rhs which is
nonlinear, e.g. abs(...), sign(...)? I suppose it's easy to consider
for the case of rhs abs(...) the system as two linear ode's, and to
switch for one to another when crossing the abs(...) from - to + and
back. But maybe there are some other possibilities to handle this
problem.

2 Consider a system of ode's. Is it possible to solve a part of the
system analytically,and the other part numerically, e.g. a Euler or
Runge Kutta integration rule. How to combine the analytical an
numerical results into one system. Maybe one can supply me with some
references/examples.

any help is greatly acknowledged.

kindest regards,
kizzie
.



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