16 citations · 39 across the 11 of their papers we have counts for
12 papers
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…
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…
Learning surrogate equations for the analysis of an agent-based cancer model
Kevin Burrage, Pamela M. Burrage, Justin N. Kreikemeyer +2
In this paper, we adapt a two-species agent-based cancer model that describes the interaction between cancer cells and healthy cells on a uniform grid to include the interaction wi…
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…
Using a library of chemical reactions to fit systems of ordinary differential equations to agent-based models: a machine learning approach
Pamela M. Burrage, Hasitha N. Weerasinghe, Kevin Burrage
In this paper we introduce a new method based on a library of chemical reactions for constructing a system of ordinary differential equations from stochastic simulations arising fr…
Stability switching in Lotka-Volterra and Ricker-type predator-prey systems with arbitrary step size
Shamika P. Kekulthotuwage Don, Kevin Burrage, Kate J. Helmstedt +1
Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis…