The Quantum and Stochastic Toolbox: xSPDE4.2

This is the fourth major release of the xSPDE toolbox, which solves stochastic partial and ordinary differential equations, with applications in biology, chemistry, engineering, medicine, physics and quantum technologies. It computes statistical averages, including time-step and sampling error estimation. xSPDE can provide higher order convergence, Fourier spectra and probability densities. The toolbox has graphical output and $\chi^{2}$ statistics, as well as weighted, projected, or forward-backward equations. It can generate input-output quantum spectra. The equations can have independent periodic, Dirichlet, and Neumann or Robin boundary conditions in any dimension, for any vector component, and at either end of any interval. xSPDE has functions that can numerically solve both ordinary and partial differential stochastic equations of any type, obtaining correlations, probabilities and averages. The toolbox has a core treating stochastic differential equations, with averages, probability distributions and full error estimates. There are stochastic extensions treating applications to partial differential equations, projected equations, quantum stochastic equations, master equations and quantum phase-space simulations including Gaussian boson sampling experiments.