基于相似结构的算法设计

Abstract

基于相似结构理论，本文对一类微分方程边值问题的求解过程进行严谨的数学推导和证明；由此提出解决这类边值问题的一种新算法——相似结构算法。相似结构算法仅仅只包含四则运算和逻辑运算，所以该算法很容易面向计算机。在文章最后，列举一个例子，根据本文所设计出来的算法利用MATLAB语言编写程序作仿真实验，且通过改变边界条件的系数来观察和分析实验结果的变化。 Based on the similar structure theory, we conduct a rigorous mathematical derivation and prove the solution procedure of a class of differential equation boundary value problems. Thus, we put forward a new algorithm to solve this kind of boundary value problem—Similar Structure Algorithm. As the similar structure algorithms only have four arithmetic and logical operations, they are easily available for the computer. An example was given at the end of this paper. Also a simulation experiment was designed by using MATLAB programming language according to the proposed algorithms. By changing the coefficients of the boundary conditions, results are observed and analyzed.