solving integral equation system for 3 unknowns

Question

Meva 2015-3-27

0
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https://ww2.mathworks.cn/matlabcentral/answers/194933-solving-integral-equation-system-for-3-unknowns

回答： Glenn Williams 2015-3-29

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