尝试求解三重积分方程时的MATLAB误差包含一个双积分

Question

我试图解决三个积分方程组来获得三个因子。方程式如下：

需要求解这些方程以获得a1，a2和amp; A3。如果它不是第三项中具有可变上限的双积分，那么使用MATLAB求解该系统相对容易。但是，只要将这个双积分输入到MATLAB代码中，我就会看到一条错误消息。 这是我的代码：

function solveIntegralForB
clc
clear all

% Extruder screw specifications

AB0=[1 1 1]
%optz1 = optimset('TolX',1e-32);
bfound = fsolve(@fminsearch,AB0)%,optz1)

      function output = fminsearch(AB)
          HH=1;


          yS1 = 0;
          yE1 = HH;
          yS2 = 0;
          yE2 = HH;
          zS3=0;
          zE3= @ (y) y;
          yS3 = 0;
          yE3 = HH;

          L1=50;
          L2=10;
          L3=0;
          %L=L';

          Inty1=integral(@Func1,yS1,yE1);
          Inty2=integral(@Func2,yS2,yE2);
          Inty3=integral2(@Func3,yS3,yE3,zS3,@ (y) y);
          %output = (L1 - Inty1)^2+(L2 - Inty2)^2;
          output(1) = (L1 - Inty1)^2;
          output(2) = (L2 - Inty2)^2;
          output(3) = (L3 - Inty3)^2;
          % factors in Eq.17 from reference
          % AB(1)=A, AB(2)=A1, AB(3)=B1

          sOut=size(output);
          function fy1 = Func1(y)
              BB=1;
              fy0=sqrt((AB(1)*y+AB(2)).^2+(BB*y+AB(3)).^2); 
              fyy=((1+fy0).^2)./(1-fy0); % F(y) in Eq.17  
              fAy=(AB(1)*y+AB(2))./(1-fy0);   
              fy1=fyy.*fAy;
          end

          function fy2 = Func2(y)
              BB=1;
              fy0=sqrt((AB(1)*y+AB(2)).^2+(BB*y+AB(3)).^2); 
              fyy=((1+fy0).^2)./(1-fy0); % F(y) in Eq.17  
              fBy=(BB*y+AB(3))./(1-fy0);   
              fy2=fyy.*fBy;                     
          end

          function fy3 = Func3(y)
              BB=1;
              fy0=sqrt((AB(1)*y+AB(2)).^2+(BB*y+AB(3)).^2); 
              fyy=((1+fy0).^2)./(1-fy0); % F(y) in Eq.17  
              fAy=(AB(1)*y+AB(2))./(1-fy0);   
              fy3=fyy.*fAy;                  
          end


      end

end

以下是错误消息：

Error using LeonExtruder/fminsearch/Func3
Too many input arguments.

Error in integral2Calc>integral2t/tensor (line 228)
        Z = FUN(X,Y);  NFE = NFE + 1;

Error in integral2Calc>integral2t (line 55)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)
    [q,errbnd] =
    integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral2 (line 106)
    Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);

Error in LeonExtruder/fminsearch (line 34)
          Inty3=integral2(@Func3,yS3,yE3,zS3,@ (y) y);

Error in fsolve (line 230)
            fuser = feval(funfcn{3},x,varargin{:});

Error in LeonExtruder (line 12)
bfound = fsolve(@fminsearch,AB0)%,optz1)

Caused by:
    Failure in initial objective function evaluation. FSOLVE
    cannot continue.