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用java實(shí)現(xiàn)二重積分的計(jì)算
目 錄
摘要 1
前言 2
1 數(shù)值積分的基本思想和存在的問(wèn)題 3
1.1 數(shù)值積分存在的某些問(wèn)題 3
1.2 數(shù)值積分的基本思想 3
2 積分方法 5
2.1 復(fù)化求積法 5
2.2 變步長(zhǎng)求積 5
2.3 1重積分和2重積分的關(guān)系 9
3 變步長(zhǎng)Simpson求2重積分 10
3.1 算法原理 10
3.2 算法實(shí)現(xiàn) 11
3.3 示例 13
4 程序的測(cè)試 14
4.1 在DOS環(huán)境下程序的運(yùn)行和調(diào)試 14
4.2 程序的測(cè)試 16
4.3 JBuilder界面上程序的演示和測(cè)試 17
5 在MATLAB中實(shí)現(xiàn)2重積分及其缺陷和JAVA的優(yōu)越性 19
5.1 在MATLAB中2重積分的實(shí)現(xiàn) 19
5.2 MATLAB的缺陷及JAVA的優(yōu)越性 22
結(jié)論 23
參考文獻(xiàn) 24
致謝 25
附錄 26
摘 要
目前數(shù)值積分存在著很多問(wèn)題，有些在形式上10分簡(jiǎn)單的函數(shù)，如： ，它的原函數(shù)不能用初等函數(shù)表示，對(duì)這類(lèi)函數(shù)就不能用牛頓—萊伯尼茲公式了；有些被積函數(shù)，其原函數(shù)雖然可以用初等函數(shù)表示成有限的形式，但表達(dá)式相當(dāng)復(fù)雜。針對(duì)上述的情況，就要求我們能夠找到1種解決2重積分計(jì)算問(wèn)題的方法。變步長(zhǎng)Simpson積分，就是1種能夠在面向?qū)ο蟪绦蛟O(shè)計(jì)語(yǔ)言編程基礎(chǔ)上實(shí)現(xiàn)2重積分計(jì)算的方法，通過(guò)Simpson積分的思想設(shè)計(jì)計(jì)算2重積分的算法，這是本設(shè)計(jì)的核心所在，并用它與MATLAB中能計(jì)算2重積分的函數(shù)進(jìn)行比較，它可以通過(guò)改變被積分函數(shù)和積分區(qū)間，能計(jì)算出任何2個(gè)積分區(qū)間是確定值的2重積分和其中第1個(gè)積分區(qū)間以函數(shù)形式給出的2重積分，這是此設(shè)計(jì)的優(yōu)越性所在，也是本設(shè)計(jì)的意義所在。再結(jié)合界面的設(shè)計(jì)、程序的運(yùn)行和演示、算法的檢測(cè)，形成1個(gè)計(jì)算2重積分的數(shù)學(xué)課件。
關(guān)鍵字：Simpson；算法；MATLAB；Java；優(yōu)越性
Abstract
A lot of problems exist in the integral of number value at present, some are even very simple in the function in form, for instance: ,original function of it can’t be expressed with elementary function and can’t use Newton—Leibnitz formula to the function; Some integrand, though its original function can show with the elementary function, the expression formula type may be quite much more complicated. To above situation , requiring us look for a kind of method that can solve the calculation problem of dual integral, turn step long Simpson integral calculus method that can realize in facing targets programming language programming and realizing the calculation problem of dual integral, it is kernel of this designed, and compared with the function that can calculate the dual integral in MATLAB with it, we can obtain this superiority designed, this is the meaning originally designed too, it can calculate any dual integral by the integrand and the block of integral through changing. Then we carry on the operation of the procedure, demonstrate and measure the algorithm and it can be come into being a mathematical courseware of calculating the dual integral.
Key words: Simpson; algorithm; MATLAB; Java; superiority.
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