matlab实验六1数值微积分与常微分方程求解

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1、实验六数值微积分与常微分方程求解、实验目的1.掌握微分与积分的数值计算方法2.掌握常微分方程的数值求解方法二、实验内容和步骤1.求函数指定点的数值导数X2Xx3f(x)=12x3x2,x=1,2,3026x2.求下列函数的导数(1)y=x,0+10v+logvl(),求y(2)y=ln(l+x),求yX=13.用数值方法求定积分⑵仕sinxf2fy+2⑷Q如歹⑶打:

2、cos(x+y'>jdxdy(1)£x2a/2x2+3dx4.求微分方程的数值解(1)y+(1.2+sinl0f)y=0,/()=0心=

3、5,y(/())=1(2)(1+t2)y+2ty+3y=2心=0占=5』仏)=0,y(/0)=1三、程序清单及运行结果1.程序清单：forx=l:1:3fx=[x,x2,x3;1,2*x,3*x2;0,2,6*x];diff(fx)end运行结果：1.(1)程序清单:x二0:0.05:1;y=x.°10+10."x+l・/loglO(x);dy=diff(y)/0.05运行结果：»Vtrninc：Locofrero.>InC：ttAILAB6^5to<>lb<>xT.atl»l.

4、oclO-«只liu«17InC：WAlLAK^5vorkVntitle4eatlifte2YornincDividebyzero.CTyp*offIUTLAB4)vi3«ByZ«ro"suppressthisyarning)>InC：«AILAKc5vorkVntitled.»吐line2dy=Coluvms1through6-12.S321-18894・1.2023-O8919-07380-06907ColuiJiz7through12・0.7468-0.9278-1.2787-1.87

5、57-2.8437・43920Coluroiz13throuch18・68872-110152-18.1724-315S42-597974-1334123Coluvms19through20•43&3387Inf(2)程序清单：x=0:0.01:1;y=log(l+x);dy=diff(y,2)/0.01;dy(99)运行结果:»ans=-0.00251.(1)程序清单:fx二inline('x."2.*sqrt(2*x.*x+3)');quad(fx,1,5)运行结果：»ans-232.8057»(2

6、)程序清单:fx=inline('x./sin(x).2');quad(fx,pi/4,pi/3)运行结果：(1)程序清单：fx二inline('abs(cos(x+y))');dblquad(fx,0,pi,0,pi)运行结果:ans-6.2832三»l_(2)程序清单：symsxy;fx=x*y;int(int(fx,y2,y+2)，-1,2);运行结果：»ans=45/8»1.(1)程序清单：建立函数文件funst.mofunctionyp=funst(t,y)yp=-(l.2+sin(10*t)

7、)*y;求解微分方程。t0=0;tf=5;yO=l;[t,y]=ode23(©funst,[tO,tf],yO)运行结果：t二1.22462.55013.864201.30822.61403.92860.06671.37142.67793.99200.13751.43472.74194.06710.20031.50012.81934.14080.26951.58422.90464.21440.35281.65302.96854.28000.43621.72193.03234.34320.50331.78

8、583.09594.41590.56631.85013.17214.48120.63691.93193.23644.54650.69131.99533.30074.60940.74572.05873.36424.68120.80812.12363.43954.75670.87382.20533.53284.83220.95912.27453.59654.89901.02772.34383.66024.96201.09632.40803.72385.00001.16002.47193.7998y=0.51

9、820.29360.18191.00000.51060.25950.15850.90350.49760.24690.13870.78220.46560.24210.12250.68230.42800.23820.11640.59840.38440.22900.11400.54020.33550.20540.11220.10800.03610.01220.00540.09740.03160.01190.00500.08640.02780.01