Collocation Methods For Neutral Delay Integro-Differential Equations

Volterra delay integro-differential equation(VDIDE) arise widely in scientific and engineering fields,such as population and biology phenomena,epidemiology,aerospace and numerical control. VDIDEs can describe rules in these fields more accurately,so they have been widely used in mathematic modeling. Because it is difficult to obtain the analytical solutions of such equations,developing the numerical methods becomes quite necessary.Collocation methods were widely used to solve differential equations and many interesting works have been done both in theoretical and practical aspects. In this thesis,we will focus on the application for solving VDIDE of neutral type (NVDIDE) .Firstly,we introduce the related background knowledge of VDIDE and collocation methods and review the developing history. Then we deal with the numerical analysis of NVDIDE with non-vanishing delay and proportional delay respectively,including construe -tion,convergence and (local) superconvergence of the designed numerical methods. In the end,by taking some NVDIDE as examples,we study the solving procedure of collocation methods,in which a special attention is paid to certain topics on the construction of numerical methods,and show the effectiveness of the methods with the numerical tests.