一维热传导方程的数值解_数学与应用数学.doc

摘要

　　　本文是通过优化的KOND算法对一维热传导方程进行数值离散化, 从而得到一维热传导方程的数值解. KOND算法的基本原理：将函数在某点用泰勒公式展开,确定泰勒展开式中各项的系数,恰当选取网格点,给出关于时间与位置的插值曲线,在网格点处建立时间插值曲线与位置插值曲线之间的函数关系.在泰勒展式中增加到了七阶,有效减少了信息的丢失,并且对边界条件进行了讨论研究，提高了数值精度.该算法所用的网格点数少，步长均匀一致.利用网格点之间的对称性，奇数项可约，减少了计算机资源的存储量，提高了计算结果的精度与计算过程的速度.该方法与其它方法比较，具有计算精度高、速度快等优点，是求解偏微分方程数值解的比较优秀的方法，也是当前对地震波探究中常采用的方法.　　

关键词：KOND算法；一维热传导方程；近似解；泰勒展开

ABSTRACT

　　　This paper carries on the numerically discretization with KOND algorithm to the One dimensional heat-conduction equation, and obtains of it. The basic principle of KOND algorithm: the function with taylor formula unfolding at some point determine the coefficient of the various expansions of taylor, Rationally choose grid point, about time and location are the location of  the function relation between the interpolation curve, add to seven order in Taylor exhibition type,  effectively reduce the loss of the information, and the boundary conditions are discussed, improve the numerical precision. The grid points in the algorithm is fewer for grid points of the algorithm,  odd items can be removed, step spacing equality and mesh points less than symmetry so algorithm reduced the reserves of computing resources and increased the computing precision. The method  has higher accuracy,  quicker speed than  central difference method so on.   It is one of good method  for numerical solution of diffifenticial equation and apply abroad to seismic prospect.

Keywords: KOND algorithm ;One-dimensional heat-conduction equation; numerical solution; Taylor expansion