再生核空间W_2~1[a,b]中线性微分方程组初值问题的数值求解

Numerical Solution for the Linear Differential Equations with Initial Conditions in Reproducing Kernel W_2~1[a,b]Space

再生核方法在某些方程(组)解的表示和逼近中具有独特的优势,用一种新的再生核讨论线性微分方程组初值问题解的精确表示与近似计算.较之以往的同类文章,对一些重要定理进行了更简单有效的证明.另外本文的再生核由于其结构简单,易于算法实现.最后的算例充分的显示了基于的再生核方法的有效性.

Reproducing kernel method owns special advantage on solving certain equations and approximate calculation, this paper uses a new reproducing kernel to discuss the exact solution and approximate calculation for the linear differential equations with initial condi- tions. Compared with the former paper of this kind, this paper gives the easier prove of some primary theorems. And because of the simple structure of the reproducing kernel, it makes the method easily achieved by procedures. The last example shows that the method based on the reproducing kernel of this paper is effective.