I need to solve a system of linear first order ODEs with boundary conditions in JAVA. I was wondering if any of you know of a JAVA package with the capability of solving a boundary value problems? (i.e. a solver using finite differences or finite elements)
The type of equation I want to solve is of the following type: $$ n''(x) = -D(x)n(x) + n'(x)/x \\ n'(0) = 0 \\ n(1) = 0 $$ Through substitution this equation can be transformed into two first order differential equations.
I know there is the ode solver of Apache commons but it can only solve initial value problems. I have also read about the numerical methods but would preferably use existing code.