Suppose I have the following boundary condition problem:
$$\frac{d^2f(x)}{dx^2}=s(x) \quad \text{for} \quad 0\le x \le L$$ $$f(0)=f_0$$ $$\alpha \frac{d f(L)}{dx} + f(L)=\beta $$
where $f_0$, $\alpha$, $\beta$ and $L$ are known real constants and $s(x)$ is a known real function.
Is it possible to describe this problem (which has a Robin boundary condition) using instead two separate new problems with Dirichlet and Neumann boundary conditions each? And later combine the solution of these two new problems to obtain the solution of the original problem.
The goal is to avoid Robin boundary conditions.