Numerically solve equations with variables inside numerical integration

Question

0 个投票

I am trying to solve equations in a form of

where C1, C2, C3 are known and

, M, F are variables to be solved. I have tried fsolve() like (below is definitely a simplified version for better illustration)

x = fsolve(@tobesolve,[0,0,0])
function rei = tobesolve(mud,M,F)
    rei(1) = integral2(@(p,theta)intfun1(p,theta,mud,M,F),0,631,0,pi)-600;
    rei(2) = integral2(@(p,theta)intfun2(p,theta,mud,M,F),0,631,0,pi)-400;
    rei(3) = integral2(@(p,theta)intfun3(p,theta,mud,M,F),0,631,0,pi)-200;
end
function i1 = int1(p,theta,mud,M,F)
i1 = p+theta+mud+M+F;
end
function i2 = int2(p,theta,mud,M,F)
i2 = p-theta-mud-M-F;
end
function i3 = int3(p,theta,mud,M,F)
i3 = p+theta-mud+M-F;
end

What is unexpected is that the error read

>> main
函数或变量 'M' 无法识别。
出错 main>@(p,theta)int1(p,theta,mud,M,F) (第 24 行)
    rei(1) = integral2(@(p,theta)int1(p,theta,mud,M,F),0,631,0,pi)-600;
出错 integral2Calc>integral2t/tensor (第 228 行)
        Z = FUN(X,Y);  NFE = NFE + 1;
出错 integral2Calc>integral2t (第 55 行)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);
出错 integral2Calc (第 9 行)
    [q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);
出错 integral2 (第 105 行)
    Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);
出错 main>tobesolve (第 24 行)
    rei(1) = integral2(@(p,theta)int1(p,theta,mud,M,F),0,631,0,pi)-600;
出错 fsolve (第 264 行)
            fuser = feval(funfcn{3},x,varargin{:});
出错 main (第 21 行)
x = fsolve(@tobesolve,[0,0,0])
原因:
    Failure in initial objective function evaluation. FSOLVE cannot continue.