Some Applications Of Spline Functions In Numerical Solutions Of Differential Equations

The research of splines derives from the middle of 20 century,and its success application in the design of shape was 1960s,until its combination with CAGD.The theory of splines have been a useful tool in the field of approximation of functions,and more and more people use splines to solve the problem in application scope,for example,data process,numerical differentiation,numerical integration,Differential Equation,integral equation,numerical solution etc.In this paper,we process the problem of numerical solution of differential equation with splines.Chapter 1 introduces univariate cubic splines and multivariate splines roughly.Chapter 2 gives some applications of univariate cubic spline in numerical solutions of ordinary differential equations,summarizes some existing methods.This chapter discusses numerical methods for two-point boundary-value problems using univariate cubic spline and using cubic B-Spline to solving 2-order boundary-value problems.Chapter 3 discusses the application of uniform B-Spline in numerical of partial differential solution.By using two series of B-Spline,a numerical method for solutions of Poission equations has been presented in this chapter.And an numerical example is presented to illustrate the efficiency of the method.Similar method may be applied in other types of partial diffenential equations.