With the enormous growth in the development of nonlinear optical devices, the complexity of the devices has increased, primarily due to the complex interplay of dispersion and nonlinearity, leading to systems which are mathematically difficult and sophisticated to fully understand and analyse. The numerical methods provide an alternative, particularly when the computing powers have increased tremendously over time, and often justify the computational cost as the number of approximations are minimised and detailed field solutions are provided with an accuracy determined primarily by the grid...