偏微分方程数值解法

2026/4/27 5:11:20

?N1Rz?N0RcosU0?dz1????tanU0?df???N1Ry?N0RsinU0??1dtanU0??dh1??df?z1df?????N1Rz?N2RcosU2?dh2dz2dtanU2

????tanU2?(?z2)dfdf???N1Ry?N2RsinU2?df

?1???2.25(2?z1?z2)?(h2?h1?z1tanU0)2?(2?z1?z2)2cosU0dz11?????tanU0??1??22dfx?10??3??2.25(h2?h1?z1tanU0)?(h2?h1?z1tanU0)?(2?z1?z2)sinU0???2.25(2?z?z)?(h?h?ztanU)2?(2?z?z)2dz212211012???df2.25(h2?h1?z1tanU0)??

其中:N0?N2?1,N1=2.25

Ry?y2?y1,Rz?d?z1?z2,R??1?????1Ry?Rz22

y1?h1?z1tanU0,y2?h2?z2tanU2 finf?h1,ffin?sinU2

function space

syms z1 z2 h1 h2 U0 U1 x3 h1=input('输入h1:'); x3=input('输入x3:'); h2=h1;

U0=input('输入U0:'); U2=input('输入U2:');

m1=sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2)*cos(U0); n1=sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2)*sin(U0); p1=2.25*(h2-h1-z1*tan(U0)); q1=2.25*(2-z1+z2);

s1=dsolve('Dz1=(-1/(tan(U0)+(q1-m1)/(p1-n1)))*(1+10(x3-10))','z1(0)=0','t1'); t1=h1;

eq1=subs(s1);

m2=sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2); n2=0; p2=p1;

q2=q1;

s2=dsolve('Dz2=-1/((q2-m2)/(p2-n2))','z2(0)=0','t2'); t2=h1;

eq2=subs(s2); s=solve(eq1,eq2)

syms z1 z2 h1 h2 U0 U1 x3 h1=input('输入h1:'); x3=input('输入x3:'); h2=h1;

U0=input('输入U0:'); U2=input('输入U2:');

m1=sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2)*cos(U0); n1=sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2)*sin(U0); p1=2.25*(h2-h1-z1*tan(U0)); q1=2.25*(2-z1+z2);

m2=sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2); n2=0;

p2=2.25*(h2-h1-z1*tan(U0)); q2=2.25*(2-z1+z2);

s1=dsolve('Dz1=(-1/(tan(U0)+((2.25*(2-z1+z2))-(sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2)*cos(U0)))/(2.25*(h2-h1-z1*tan(U0))-(sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2)*sin(U0)))))*(1+10(x3-10)),Dz2=-1/(((2.25*(2-z1+z2))-(sqrt((h2-h1-z1*tan(U0))^2+(2-z1+z2)^2)))/((2.25*(h2-h1-z1*tan(U0)))))','z1(0)=0','z2(0)=0')


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