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| 折扣與優(yōu)惠：團(tuán)購最低可5折優(yōu)惠 - 了解詳情 | 論文格式：Word格式(*.doc) |  |
摘要 本文是通過優(yōu)化的KOND算法對一維熱傳導(dǎo)方程進(jìn)行數(shù)值離散化, 從而得到一維熱傳導(dǎo)方程的數(shù)值解. KOND算法的基本原理：將函數(shù)在某點(diǎn)用泰勒公式展開,確定泰勒展開式中各項(xiàng)的系數(shù),恰當(dāng)選取網(wǎng)格點(diǎn),給出關(guān)于時(shí)間與位置的插值曲線,在網(wǎng)格點(diǎn)處建立時(shí)間插值曲線與位置插值曲線之間的函數(shù)關(guān)系.在泰勒展式中增加到了七階,有效減少了信息的丟失,并且對邊界條件進(jìn)行了討論研究，提高了數(shù)值精度.該算法所用的網(wǎng)格點(diǎn)數(shù)少，步長均勻一致.利用網(wǎng)格點(diǎn)之間的對稱性，奇數(shù)項(xiàng)可約，減少了計(jì)算機(jī)資源的存儲量，提高了計(jì)算結(jié)果的精度與計(jì)算過程的速度.該方法與其它方法比較，具有計(jì)算精度高、速度快等優(yōu)點(diǎn)，是求解偏微分方程數(shù)值解的比較優(yōu)秀的方法，也是當(dāng)前對地震波探究中常采用的方法. 關(guān)鍵詞：KOND算法；一維熱傳導(dǎo)方程；近似解；泰勒展開
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
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