Retarded differential equations

Retarded differential equations (RDEs) are differential equations having retarded arguments. They arise in many realistic models of problems in science, engineering, and medicine, where there is st time lag or after-effect. Numerical techniques for such problems may be regarded as extensions of dense-output methods for ordinary differential equations (ODEs), but scalar RDEs are inherently infinite dimensional with a richer structure than their ODE counterparts. We give background material, develop a theoretical foundation for the basic numerics, and give some results not previously published. (C) 2000 Elsevier Science B.V. All rights reserved.