3 papers
math.NA2025
Implementation of Milstein Schemes for Stochastic Delay-Differential Equations with Arbitrary Fixed Delays
Mitchell T. Griggs, Kevin Burrage, Pamela M. Burrage
This paper develops methods for numerically solving stochastic delay-differential equations (SDDEs) with multiple fixed delays that do not align with a uniform time mesh. We focus…
math.NA2025
Magnus Methods for Stochastic Delay-Differential Equations
Mitchell T. Griggs, Kevin Burrage, Pamela M. Burrage
This paper introduces Magnus-based methods for solving stochastic delay-differential equations (SDDEs). We construct Magnus--Euler--Maruyama (MEM) and Magnus--Milstein (MM) schemes…
math.NA2023
A spectrally accurate step-by-step method for the numerical solution of fractional differential equations
L. Brugnano, K. Burrage, P. Burrage +1
In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step graded mesh procedure based on an expansion of the vec…