用Matlab求贝塞尔函数的根.doc

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1、用Matlab求贝塞尔函数的根clearclcR=1;maxv=5;maxs=5;j=zeros(maxv,maxs);%用于存放第一类贝塞尔函数的根，同一行阶数相同，列数表示第几个根incr=4.0;forv=0:maxv-1h=v+1.9*v^(1/3)+1;if(v==0)j(v+1,1)=fzero(@(x)besselj(v,x),2);elsej(v+1,1)=fzero(@(x)besselj(v,x),h);endfors=2:maxsj(v+1,s)=fzero(@(x)besselj(v,x),j(v+1,s-1)+incr)

2、;endendjmaxv1=5;maxs1=5;jd=zeros(maxv1,maxs1);%用于存放导数的根incr1=3.0;forv1=0:maxv1-1h1=v1+2;if(v1==0)jd(v1+1,1)=fzero(@(x)besseld(v1,x),3);elsejd(v1+1,1)=fzero(@(x)besseld(v1,x),h1);endfors=2:maxs1jd(v1+1,s)=fzero(@(x)besseld(v1,x),jd(v1+1,s-1)+incr1);endendjdlanmda=zeros(1,maxs*

3、maxv+maxs1*maxv1);form=1:maxsforn=1:maxvlanmda((m-1)*maxs+n)=2*pi*R/j(m,n);endendform=1:maxs1forn=1:maxv1lanmda(maxs*maxv+(m-1)*maxs1+n)=2*pi*R/jd(m,n);endend'排序前的波长:'lanmdaN=length(lanmda)form=1:Nforn=1:N-miflanmda(n)

4、t;endendend'排序后的波长:'Lanmda执行结果：j=2.40485.52018.653711.791514.93093.83177.015610.173513.323716.47065.13568.417211.619814.796017.95986.38029.761013.015216.223519.40947.588311.064714.372517.616020.8269jd=3.83177.015610.173513.323716.47061.84125.33148.536311.706014.86363.05426.70

5、619.969513.170416.34754.20128.015211.345914.585817.78875.31769.282412.681915.964119.1960ans=排序前的波长:lanmda=Columns1through82.61271.13820.72610.53290.42081.63980.89560.6176Columns9through160.47160.38151.22350.74650.54070.42470.34980.9848Columns17through240.64370.48280.38730.323

6、70.82800.56790.43720.3567Columns25through320.30171.63980.89560.61760.47160.38153.41261.1785Columns33through400.73610.53670.42272.05720.93690.63020.47710.3844Columns41through481.49560.78390.55380.43080.35321.18160.67690.4954Columns49through500.39360.3273N=50ans=排序后的波长:lanmda=C

7、olumns1through83.41262.61272.05721.63981.63981.49561.22351.1816Columns9through161.17851.13820.98480.93690.89560.89560.82800.7839Columns17through240.74650.73610.72610.67690.64370.63020.61760.6176Columns25through320.56790.55380.54070.53670.53290.49540.48280.4771Columns33through

8、400.47160.47160.43720.43080.42470.42270.42080.3936Columns41through48