Two Kinds Of Effective Methods To Solve Differential Equations

In the paper, we study two kind of diferential equation, including integral-diferential equation and neutral delay diferential equation. These models are oftenapplied to the mechanics、physics、biology、engineering and computational math-ematics, etc.Firstly, this paper analyse integral-diferential equation with boundary condi-tions in reproducing kernel space. At the same time, it is discuss that the analysismethod of reproducing kernel space to the stability of the solution. Secondly, ho-motopy analysis method is applied to neutral diferential function with proportionaldelay. Linear equation is a simple equation relatively. There are many methods tosolve this equation. The paper introduces the homotopy analysis method to getbetter numerical approximate solution. Meanwhile, the method is efective to solvenonlinear problem, some methods can not obtain a better result to approximatesolution. In this paper, the homotopy analysis method is applied to linear neutraldiferential equation with proportional delay, and the method is also applied to arare nonlinear neutral diferential equation with proportional delay. The solve is noteasy to get about this kind of equation, and its result also is not very ideal. Thispaper make use of the homotopy analysis method to solving the nonlinear problem.It is get a numerical approximate solution. It is shows that the two kinds of themethod by the approximate solution.