How to estimate three parameters in BVP5C

Question

Jacob Jepson 2021-11-1

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1576648-how-to-estimate-three-parameters-in-bvp5c

I am trying to estimate three (unknown) parameters, c, N_0 and C_0 using BVP5C. The boundary problem I wish to solve consists of 4 first order ODEs, and 7 boundary conditions (4 for the variables, 3 required for the unknown parameters). Here is my code

xmesh = linspace(-50,-0.001,1000);
p = [0.3 0.01 0.5];
solinit = bvpinit(xmesh, @guess, p);
sol = bvp5c(@bvpfcn, @bcfcn, solinit);
Y=sol.y;
C=sol.parameters;
figure(5)
hold off
plot(sol.x, Y(2,:),sol.x, Y(4,:),'LineWidth',2)
function dydx = bvpfcn(~,y,c) % equation to solve
kappa = 2; sigma=0.01;
dydx = [(-c*y(1)-y(1)^2)/y(2)-kappa*(1-y(2))*y(4)+(1-y(4));
    y(1);
sigma*y(2)*y(4);
   y(3)];
end
%--------------------------------
function res = bcfcn(ya,yb,c,N_0,C_0) % boundary conditions
C_inf = 0.8; sigma = 0.01; M=50; kappa=2; gamma=-kappa*C_inf-1+C_inf;
res = [ ya(1)-gamma*N_0*exp(M*gamma/c)/c;
        ya(2)-N_0*exp(M*gamma/c);
       ya(3)-sigma*N_0*exp(M*gamma/c);
       ya(4)-sigma*N_0*exp(M*gamma/c)-C_0;
       yb(1)+c;
       yb(2);
       yb(4)-C_inf;
       ];
end
function g = guess(x)
g=[  -(x+1)*exp(x); 
    -x*exp(x);
    0.5*exp(x);
    0.5*(1+exp(x));
    ];
end 

and I recieve the error message

Not enough input arguments.
Error in StefanCompetitionBVP>bcfcn (line 22)
res = [ ya(1)-gamma*N_0*exp(M*gamma/c)/c;
Error in bvparguments (line 106)
    testBC = bc(ya,yb,bcExtras{:});
Error in bvp5c (line 137)
    bvparguments(solver_name,ode,bc,solinit,options);
Error in StefanCompetitionBVP (line 5)
sol = bvp5c(@bvpfcn, @bcfcn, solinit);