数理方程近似求解的数论方法  

THE APPROXIMATE SOLUTION OF EQUATIONS OF MATHEMATICAL PHYSICS BY NUMBER THEORETIC METHODS

作　　者：王元[1] 徐广善[1] 杨照华[2] 

机构地区：[1]中国科学院教学研究所,北京100080 [2]华南师范大学数学系,广州510631

出　　处：《应用数学学报》1999年第4期541-547,共7页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金

摘　　要：本文，我们用数论网格建议了一个求解数学物理方程的近似方法，此处Fn表示Fibonacci贯．若初始函数适当光滑，本文将给出误差估计，两个例子都表明这一方法优于经典网格方法．In this paper, we propose a method by the use of number-theometic net is contract the difference equations of the equations of mathematical physics, where Fn denotes the Fibouacci sequence. The error estimation will be given when the initical function satisfies some smooth conditions. We give also two examples which all show that this method is better than the classical method obtained by equi-distributed net.

关 键 词：数理方程 数论方法 柯西问题 近似解 热传导方程 

分 类 号：O175.24[理学—数学] O411.1[理学—基础数学]