# Tag Info

1 - The Neumann boundary condition is actually named after Carl Neumann, not John von Neumann. There is another boundary condition not often mentioned but used very often in practice in Quant finance FD solvers, which is linear (zero second spatial derivative on the boundary). This means that on the boundary the PDE $a\frac{\partial U}{\partial x} + b \frac{... 3 Yes it should preserve positivity. However due to numerical noise you may observe very small negative values on the edges of the lattice, that you can truncate to zero. If you solve using Fokker-Planck you may want to start from$t=\delta t\$ using a gaussian approximation for the density on the first step, so as to start from a smooth density. An alternative ...