matlab 数值积分.htm

数值计算方法

                %GAUSS10(fun,a,b) 利用 10 参数 Gauss 求积法近似计算 a&lt;x&lt;b 区间上的积分<br>
                % fun 被积函数。字符串、内联函数名、 M 函数文件名都可。<br>
                %======================================================<br>
                x = [0.1488743390;0.4333953941;0.6974095683; ...<br>
                0.8650633667;0.9739065285];<br>
                w = [0.2955242247;0.2692667193;0.2190863625; ...<br>
                0.1494513492;0.0666713443];<br>
                t = .5*(b+a)+.5*(b-a)*[-flipud(x);x];<br>
                W = [flipud(w);w];<br>
                g = sum(W.*feval(fun,t))*(b-a)/2;<br>
                <br>
                【 * 例 5.8.1 .2-1 】当 <img alt=MATLAB 数值积分 src="http://www.itfat.com/picnet/200410/0511815571185004.gif">时，比较解析积分和近似积分。<br>
                <br>
                （1）用符号法求解：<br>
                syms x;F=int(&#39;cos(x)&#39;,&#39;x&#39;,-1,1),vpa(F) <br>
                F =    <font color=#F0F1F3>计算机教程MATLAB 数值积分来自www.itwen.com</font> <br><br>
                2*sin(1)<br>
                ans =<br>
                1.6829419696157930133050046432606<br>
                <br>
                （2）用式 ( 5.8.1 .2-4) 近似计算：<br>
                aF=cos(1/sqrt(3))+cos(-1/sqrt(3)) <br>
                aF = <br>
                1.6758<br>
                <br>
                【 * 例 5.8.1 .2-2 】求 <img alt=MATLAB 数值积分 src="http://www.itfat.com/picnet/200410/0511815571158657.gif">，准确结果是 <img alt=MATLAB 数值积分 src="http://www.itfat.com/picnet/200410/0511815571269807.gif">。<br>
                <br>
                （1）符号法<br>
                syms x;IS=int(&#39;sqrt(log(1/x))&#39;,&#39;x&#39;,0,1) <br>
                Warning: Explicit integral could not be found. <br>
                &gt; In D:\MAT53\toolbox\symbolic\@sym\int.m at line 58<br>
                In D:\MAT53\toolbox\symbolic\@char\int.m at line 9<br>
                IS =<br>
                int(log(1/x)^(1/2),x = 0 .. 1)<br>
                <br>
                （2）用 quad 指令求积<br>
                ff=inline(&#39;sqrt(log(1./x))&#39;,&#39;x&#39;);Isim=quad(ff,0,1) <br>&nbsp;&nbsp;&nbsp;本篇文章共7页，此页为第2 页&nbsp;&nbsp;&nbsp;<a href=17929.html>上一页</a>&nbsp;&nbsp;&nbsp;<a href=17929_3.html>下一页</a></P></font><br>
  			
			
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