solving integral equation system for 3 unknowns
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Hi guys,
I need to solve integral equations : The equations are kutta, lateral, angular. Unknons are h4, theta4, c13. I used brute force algorithm. but it gives me error. I assume the error comes from integral upper bouns being x!!
beta1=0.2;
alphabar=-0.1;
theta4range=-1:0.1:4;
h4range=0:0.1:1;
c13range=-1:0.1:1;
% c23=-c13;
rmass=1.0;
rmomi= 2.0;
a = 0.1;
x=linspace(0,1,101);
thickness= a*sin(pi*x);
eps=0.01;
hassolution=0;
for theta4=theta4range
for h4=h4range
for c13=c13range
% syms x;
H0=@(x) 1/(2*(1-thickness));
H14 =@(x)(-h4-theta4.*(x-1/2));
H24 =@(x)(h4 + theta4.*(x-1/2));
u13=@(x)1./H0 *( -4 * integral(H14,0,x) +c13);
u23=@(x)1./H0 *(-4 * integral(H24,0,x) -c13);
velocitydifference= @(x)1./H0 * (-4 * integral(H24,0,x) -c13)- ...
(1./H0 * (-4 * integral(H14,0,x) +c13)) ;
p12 = @(x) -3 * integral(u13,0,x);
p22 = @(x) -3 * integral(u23,0,x);
pressuredifference=@(x) -3 * integral(u23,0,x) - (-3 * integral(u13,0,x));
kutta = 3 * integral(velocitydifference,0,1)+beta1*alphabar;
lateral = integral(pressuredifference,0,1)-12*rmass*h4;
angular = integral((x-1./2).*(pressuredifference),0,1)-12*rmomi*theta4;
if abs(kutta)<eps && abs(lateral)<eps && abs(angular)<eps
c13
theta4
h4
hassolution=1;
end
end
end
end
if ~hassolution
disp('No solution');
end
回答(1 个)
Glenn Williams
2015-3-29
I have solved this system. Please refer to our Guru.com agreement for further details.
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