The Numerical Solution Of Delay Differential Equations Via Reproducing Kernel Theory

In this thesis,the main problem is how to solve linear and nonlinear delay equa-tions by use of the theory of reproducing kernel.The first chapter discussed the gen-eral developing progress of delay equations and reproducing kernel.The second chap-ter give the main characterization about reproducing kernel.Through this chapter,weknow the base theory of the reproducing kernel.In the third chapter we use the repro-ducing kernel theory to solve linear neutral delay differential equations,from whichwe know the exact solution and numerical solution ,and the error is well. We con-clude that the possibility of this method, In the last chapter we use this theory to solvenonlinear pantograph delay equations and the result is also good.Since we have knownmuch about reproducing kernel,There are still many fields we should to study aboutit.