工程设计近似计算精度的探索

研究了一个新的积分不等式及它的应用,它具有传统积分近似计算所不具备的高精度特点,介绍了用新的积分不等式求解定积分 ∫xb=cosx/x3dx的近似值,当积分上限X远离下限b时,不等式的不等程度增大,反之,当X趋近于b时,其不等程度趋于0,也就是说积分区间分得愈细,其积分误差愈小.这样,借助于计算机运算,几乎能将积分的近似值很容易地转换成精确值,无论是什么样的工程设计计算,计算机都能在快速计算的同时大幅度提高近似计算的精度,开创了工程设计计算的新时代.

Exploration on accuracy of approximate computation in engineering design

In this paper, we have studied the following integral inequality and its application, which has the advantage over the traditional approximate integration＇s computation of high- accuracy. The integral inequality is used to figureout approximation of definite integrationdx accurately. The d unequal degree of equations is increasing whilethe upper of integrations X is far away from lower value B. Conversely, when X is set close to B,it approaches zero. In other words, the narrower the region of integration is separated, the less the error is. Therefore, with the help of computer, the approximation of integration can be easily converted into accuracy value. No matter how complicated the engineering design computation is, the computer can figure it out rapidly as well as improve the accuracy simultaneous- ly, which initiates a new a~e of en~ineerino de,~ic~n ~＇nmn~Itat~nn