Delay differential equations
This article concerns delay-differential equations (DDEs) with constant lags. DDEs increasingly are being used to model various phenomena in mathematics and the physical sciences. For such equations the value of the derivative at any time depends on the solution at a previous "lagged" time. Although solving DDEs is similar in some respects to solving ordinary differential equations (ODEs), it differs in some rather significant ways. These differences are discussed briefly. The effect the differences can have on systems of ODEs and DDEs is illustrated. Popular approaches used in the development of numerical methods for solving DDEs are described. Available Matlab DDE solvers and a Fortran 90 solver based on these approaches are mentioned. Finally, some pointers to further resources available to interested readers are given.
Shampine, Lawrence and Thompson, Skip
"Delay-Differential Equations with Constant Lags,"
Vol. 9, Article 10.
Available at: http://scholarship.claremont.edu/codee/vol9/iss1/10