ISSN:
1572-9125
Keywords:
AMS(MOS): 65L20
;
CR: 5.17
;
delay differential equations
;
numerical solution
;
Runge-Kutta methods
;
interpolation procedures
;
stability
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU′(t)=λU(t)+μU(t−τ) with λ, μ ε C, Re(λ)〈−|μ|, and τ〉0. Ifc i denotes theith abscissa of a given Runge-Kutta method, then in thenth stept n−1→t n :=t n−1+h of the numerical process our interpolation procedure computes an approximation toU(t n−1+c i h−τ) from approximations that have already been generated by the process at pointst j−1+c i h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01994847
