NUMERICAL-SOLUTION BY LMMS OF STIFF DELAY-DIFFERENTIAL SYSTEMS MODELING AN IMMUNE-RESPONSE

We consider the application of linear multistep methods (LMMs) for the numerical solution of initial value problem for stiff delay different ial equations (DDEs) with several constant delays, which are used in m athematical modelling of immune response. For the approximation of del ayed variables the Nordsieck's interpolation technique, providing an i nterpolation procedure consistent with the underlying linear multistep formula, is used. An analysis of the convergence for a variable-steps ize and structure of the asymptotic expansion of global error for a fi xed-stepsize is presented. Some absolute stability characteristics of the method are examined. Implementation details of the code DIFSUB-DDE , being a modification of the Gear's DIFSUB, are given. Finally, an ef ficiency of the code developed for solution of stiff DDEs over a wide range of tolerances is illustrated on biomedical application model.