Some nonlinear PDEs partial differential equations are exactly solvable. As an example, nonlinear PDEs such as the Soliton equation were shown to be exactly solvable by quantum operator methods. More recently the Boltzmann equation was solved exactly as well. A question is are other equations...

The paper proposes a new automatic/algorithmic differentiation for the solutions to partial differential equations of parabolic type. In particular, we provide a higher order discretization scheme which is a natural extension of the standard automatic differentiation. A Brownian polynomial...