An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations

By Desmond John Higham. SIAM Review, 2001

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Extinction and recurrence of multi-group SEIR epidemic (2013, methodology): “Using the Milstein’s higher order method ([26]), we simulate the positive solution to Eq.”
DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia (2017, background): “However, a user who is familiar with standard ODE tools has to “leave the box” to find a new specialized package to handle these kinds of differential equations, or write their own solver scripts [9].”
Stochastic persistence and stationary distribution in a Holling–Tanner type prey–predator model (2012, methodology): “The relations between the white noise terms and Wiener processes are defined by dBr = ξr(t)dt, r = 1, 2 [79].”
A model of interval timing by neural integration (2011, neutral): “1d) by the Euler–Maruyama method (Higham, 2001).”
A brief introduction to pseudospectral methods : application to diffusion problems (2016, neutral): “4) using the Euler–Maruyama method [21], for example (3) Compute the solution value using representation (D.”