Using The Reproducing Kernel Method For Solving A Class Of Singularly Perturbed Delay Differential Equations

Singular perturbed delay problem of di?erential equation appears widely in dynamics. In the past, scholars always ignore the minimizing delay when they faced with this problems, this manner for this problems can not satisfied with the practical matters, in some problems with high precision requirements, the results of the singular perturbed delay problems will become bad when we use this manner, we don’t want to see this obviously, so, it is necessary to find a useful numerical treatment to deal with this problems. some scholars have used the reproducing kernel method to deal with singular perturbed problems and delay problems respectively, however, there are very a few work on singular perturbed delay problems, so this paper use that set as a starting point to give out a useful numerical method.This paper focuses on combine the reproducing kernel space method with some other methods and techniques to deal with singular perturbed delay problems. the paper will move freely, combined with some examples to talk about the accuracy and the stability of this method.In the first chapter, the paper introduces the history of singular perturbed delay problems, expressed the research status and the research significance of this problems,then talk about the status of the reproducing kernel method and its history.The second chapter mainly introduces how to use reproducing kernel method to deal with some boundary value problem of di?erential, then, give a new error estimation method.The third chapter firstly introduces the research significance of singular perturbed delay problems; and then gives out two useful reproducing kernel methods with some other methods and techniques to solve this problems. After that, the paper give the series expression of solution. At last, combined with some examples to talk about the accuracy and the convergence of the two methods.In the fourth chapter, the paper introduces the research significance of delay problems, expressed how to use reproducing kernel method to solve this problems, and provides the accurate solution and approximate solution, then use some numerical examples which verified the superiority of the reproducing kernel space.The fifth chapter mainly studies the solution method of singular perturbed delay problems, and lists out the form of approximate solution by using the theory of reproducing kernel, using some examples to express how to solve practical problems by using this method, and proved the convergence and the stability of this method,The sixth chapter summarizes all the content of this paper, and puts forward some improved suggestion to study the method for the future.