偏微分方程组MATLAB数值解.docx

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1、偏微分方程求解1.具体方程实例已知：v=12z0= 0 =16,o= axGj =11727.24539, G2 =11997.20618, G3 =12075.482870=h=7,R=2,G4 =12153.75956 ,G5 = 12232.03625, G6 = 12310.31294 , G=9800,T1cos0 = Fw = 0.625 * / * 2RaG：+422GKcos(/2 + e)= 7；21 2GzG： + T： -2Gl03sg2 + G = T；-2G2T2G；+7；22G/cos(7r/2 + e)= 7；22GzG：+7；2G4 cos(/2 + e)= 7

2、；22G4T4G；+22G54cos(万/2 + 9) = 7；2G； + 年 一 2Gcos ( / 2 + 8)=qcos%+G浮=pgR*(2-a)T6sinor5 =)cos。cos% +cos% + cos ay +cos% + cos a5 +(2 。)= 2 .方程代码function eq=myfun(X)TOW);a=X(2);T1二X ；T2=X(4);a2=X(5);T3=X(6);a3=X(7);T4=X(8);a4=X(9);T5=X(10);a5=X(ll);T6=X(12);cta=X(13);al=X(14);h=X(15);% 初值设置v=12;R=2;Gl=

3、11727.24539;G2=11997.20618;G3=12075.48287;G4=12153.75956;G5=12232.03625;G6=12310.31294;G7=9800; %即是 G 浮g=9.8;rp=1025;eq(l)=T0*cos(cta)-0.625*(vA2)*2*R*a;eq(2)=GlA2+T0A2-2*Gl*T0*cos(pi/2+cta)-TlA2;eq(3)=cos(al)-(GlA2+TlA2-T0A2)/(2*Gl*Tl);eq(4)=G2A2+T0A2-2*G2*T0*cos(pi/2+cta)-T2A2;eq(5)=cos(a2)-(G2A2+

4、T2A2-T0A2)/(2*G2*T2);eq(6)=G3A2+T0A2-2*G3*T0*cos(pi/2+cta)-T3A2;eq(7)=cos(a3)-(G3A2+T3A2-T0A2)/(2*G3*T3);eq(8)=G4A2+T0A2-2*G4*T0*cos(pi/2+cta)-T4A2;eq(9)=cos(a4)-(G4A2+T4A2-T0A2)/(2*G4*T4);eq(10)=G5A2+T0A2-2*G5*T0*cos(pi/2+cta)-T5A2;eq(ll)=cos(a5)-(G5A2+T5A2-T0A2)/(2*G5*T5);eq(12)=G6A2+T0A2-2*G6*T0*

5、cos(pi/2+cta)-T6A2;eq(13)=T6*cos(a5)+G7-rp*g*pi*(RA2)*(2-a);eq(14)=T6*sin(a5)-T0*cos(cta);eq(15)=cos(al)+cos(a2)+cos(a3)+cos(a4)+cos(a5)+(2-a)-h;主程序：close all;clear all;cic;%solve调用最好的方法，适合多个方程多个变量的情况close all;clear all;de;% 已知量%syms VRG1G2 G3 G4 G5 G6 G7 g rp;% 已知量v=12;R=2;Gl=11727.24539;G2=11997.2

6、0618;G3=12075.48287;G4=12153.75956;G5=12232.03625;G6=12310.31294;G7=9800; %即是 G 浮g=9.8;rp=1025;syms TO a T1T2 a2 T3 a3 T4 a4 T5 a5 T6 eta al h;%变量约束%15 个等式eql=T0*cos(cta)-0.625*(vA2)*2*R*a;eq2=GlA2+T0A2-2*Gl*T0*cos(pi/2+cta)-TlA2;eq3=cos(al)-(GlA2+TlA2-T0A2)/(2*Gl*Tl);eq4=G2A2+T0A2-2*G2*T0*cos(pi/2+

7、cta)-T2A2;eq5=cos(a2)-(G2A2+T2A2-T0A2)/(2*G2*T2);eq6=G3A2+T0A2-2*G3*T0*cos(pi/2+cta)-T3A2;eq7=cos(a3)-(G3A2+T3A2-T0A2)/(2*G3*T3);eq8=G4A2+T0A2-2*G4*T0*cos(pi/2+cta)-T4A2;eq9=cos(a4)-(G4A2+T4A2-T0A2)/(2*G4*T4);eql0=G5A2+T0A2-2*G5*T0*cos(pi/2+cta)-T5A2;eqll=cos(a5)-(G5A2+T5A2-T0A2)/(2*G5*T5);eql2=G6A2

8、+T0A2-2*G6*T0*cos(pi/2+cta)-T6A2;eql3=T6*cos(a5)+G7-rp*g*pi*(RA2)*(2-a);eql4=T6*sin(a5)-T0*cos(cta);eql5=cos(al)+cos(a2)+cos(a3)+cos(a4)+cos(a5)+(2-a)-h;W=solve(eql,eq2,eq3,eq4zeq5,eq6/eq7/eq8/eq9,eql0/eqll,eql2/eql3,eql4/eql5);%endclose all;clear all;cic;%solve调用方法一syms R N a h x w;R N a h x w=solv

9、e(360-180*h=R*cosh(log(tan(a)+sec(a)*cos(a),.5880=R*cosh(log(tan(a)+sec(a)*sin(a)+N,.30324.63=N+2891.44+126229.2*h,.,360-180*h=R*cosh(68.R*x+log(tan(a)+sec(a)*cos(w),.tan(w)=68.6*sinh(68./R*x+log(tan(a)+sec(a),.,sinh(68,R*x+log(tan(a)+sec(a)-R/58.6*tan(a)=22.05/R, N, a ,h, x, w);R=eval(R)h=eval(h)%s

10、olve调用方法二syms x y z I;eql=0.5*9.8*0.6A?/pi*tanh(2*pi*0.?/x)-x;eq2=0.142*x*tanh(2*pi*0.2/x)-y;eq3=0.25*y*(sinh(2*2*pi*0.yx)+2*2*pi*0.yx)/(sinh(2*pi*0.?/x)A2-z;eq4=pi*zA).6-l;I x y Z=solve(eql/eq2zeq3/eq4zl,x7y7z,);l=eval(l)x=eval(x)y=eval(y)z=eval(z)close all;clear all;cic;syms xy zl;eql=0.5*9.8*0.6A2/pi*tanh(2*pi*0.2/x)-x;eq2=0.142*x*tanh(2*pi*0.yx)-y;eq3=0.25*y*(sinh(2*2*pi*0.?/x)+2*2*pi*0.yx)/(sinh(2*pi*0.?/x)A2-z;eq4=pi*zA).6-l;W=solve(eql/eq2/eq3/eq4/r/x7y7z,);l=eval(W.I)x=eval(W.x)y=eval(W.y)z=eval(W.z)