The differential operator $ D_{0} $ discretizes the
first derivative with the second-order formula
$$ \frac{\partial u_{i}}{\partial x} \approx
\frac{u_{i+1}-u_{i-1}}{2h} = D_{0} u_{i}
$$
test
the correctness of the returned values is tested by
checking them against numerical calculations.
solve linear system for a given right-hand side
without result Array allocation. The rhs and result parameters
can be the same Array, in which case rhs will be changed
$ D_{0} $ matricial representation
The differential operator $ D_{0} $ discretizes the first derivative with the second-order formula $$ \frac{\partial u_{i}}{\partial x} \approx \frac{u_{i+1}-u_{i-1}}{2h} = D_{0} u_{i} $$
the correctness of the returned values is tested by checking them against numerical calculations.