Application Of B-theory Of Numerical Methods For Functional Differential Equations To Stiff Delay Differential Equations

The paper is devoted to theory of stability and convergence of numeical methods for initial value problems in nonlinear stiff delay differential equations (DDEs) and to efficient numerical methods for DDEs. Main results in this paper are as follows.(1) Applying B- theory of numerical methods for stiff Volterra functional differential equations(VFDEs) to the special case of nonlinear stiff DDEs, we get a series of new stability and convergence results of numerical methods for DDEs which are more general and deeper than the existing related results in literature.(2) Following the theory obtained in the present paper, we recommend some classes of efficient numerical methods for stiff DDEs , as well as for the general VFDEs.(3) Applying the efficient numerical methods recommended above to solve nonlinear stiff DDEs, and more generally, to solve delay integro-differential equa-tions(DIDEs), we have done a series of numerical experiments, which not only support the theory obtaind in this paper but also demonstrat the efficiency of the recommended numerical methods, and provide techniques for choosing numeical methods for the large scale stiff computation that appear in various scientific and engineering practical problems.