The Application Of Multi-grid Of Finite Volume For Solving Two-point Boundary Value Problem

Differential equations of two-point boundary value problems have been widely applied in many fields,such as science,engineering,medicine,life sciences and so on.In the process of solving,it is very important to find a numerical method with fast converging speed and high precision. This paper studies a class of two-point boundary value problems with linear delay differential equations. The quadratic convergences is obtained through constructing a finite volume method and analyzing its error. On the basis of it, the four-order convergence of numerical methods is obtained through multi-grid technology.The main research work;(1) Firstly, the interval is divided into a set of small interval.Then, the finite volume scheme is obtained by integrating the equation on each small interval and using the linear discrete interpolation method. Moreover, the errors of the numerical solution, such as discrete H1semi-norm error,L2 norm error and maximum norm error,are analyzed,which shows the finite-volume scheme is two-order convergent.(2) Based on the finite-volume scheme, a extrapolating finite-volume scheme is obtained through twice integrating the equation on discrete error and using the linear discrete interpolation method. Error analysis shows the new alorithm has higher precision. The four-order convergence of this new scheme is proved by theory analysis.(3) This paper gives some numeircal examples of solutions to linear delay differential equations by using extrapolating finite-volume scheme and the finite-volume method.The experiment results verify the effectiveness and convergence of these methods.