Finite difference (FD) methods are a set of numerical schemes that approximate the solutions to differential equations. They use a fixed time step and grid points to approximate derivatives. Although some FD methods have nice consistency and stability qualities, they often break down when it comes to the algebraic properties of the solution. Two such properties are that of elementary stability and positivity. Elementary stability means that the steady states of the numerical approximation match and have the same stability as the steady states of the theoretical solution. Positivity means that if the initial condition is nonnegative then all values of the solution for time t>0 should be nonnegative as well.

 Nonstandard finite difference (NSFD) methods are a subclass of FD methods which contort the step size to ensure that the properties we care about (e.g. elementary stability and positivity) are maintained. We are particularly interested in NSFD for PDEs.