变系数线性微分方程数值解的矩阵法

IF 1.4 4区工程技术 Q2 ENGINEERING, AEROSPACE

Aeronautical Journal Pub Date : 1957-02-01 DOI:10.1017/S0368393100130901

E. A. Winn

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引用次数: 0

摘要

本文导出了一种求解线性微分方程的方法，该方法不需要特殊的起始程序，并且至少在原则上能够扩展到任何精度级别。该方法的另一个优点是边界条件很容易满足，并且只在输入函数中不同的方程组的解需要很少的额外计算。这种方法需要一个矩阵的往复，其阶数等于要得到解的点的数目，但这可以通过适当地划分矩阵而大大简化，并且对于大多数自动高速计算机来说，矩阵的往复在任何情况下都是一种容易编程的操作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Matrix Method for the Numerical Solution of Linear Differential Equations with Variable Coefficients

A method of solution of linear differential equations is derived which requires no special starting procedure, and which is, in principle at least, capable of extension to any order of accuracy. Further advantages of the method are that boundary conditions are easy to satisfy, and that the solution of families of equations differing only in the input function requires little extra computation. The method requires the reciprocation of a matrix of order equal to the number of points for which a solution is to be obtained, but this can be much simplified by suitably partitioning the matrix, and with most automatic high-speed computers the reciprocation of a matrix is in any case an easily programmed operation.

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来源期刊

Aeronautical Journal 工程技术-工程：宇航

CiteScore

3.70

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： The Aeronautical Journal contains original papers on all aspects of research, design and development, construction and operation of aircraft and space vehicles. Papers are therefore solicited on all aspects of research, design and development, construction and operation of aircraft and space vehicles. Papers are also welcomed which review, comprehensively, the results of recent research developments in any of the above topics.