MATLAB: Initial guess for bvp4c

bvp45initial guess

rsco=0.0024 %Reference SC resistance at h0 mmHg/(μl/min)
rje = 2.08 %mmHg/(μl/min)
rd=0.694 %mmHg/(μl/min)
beta=rje/rsco
x=0:0.01:1; %μm
pac=15 %mmHg
pev=9 %mmHg
fi=rje/rd
%""you must provide an initial guess for the solution ?? here there is the
%problem everything else seems to be correct""
%–> suggestion from Matlab A: crude mesh of five points and a constant
%guess that satisfies the boundary conditions are good enough to get
%convergence on the interval
infinity = 1;
maxinfinity = 2;
solinit = bvpinit(linspace(0,infinity,2),[25 0 0]); %don't know how to manage it
sol = bvp4c(@fsode,@fsbc,solinit);
function dfdeta = fsode(y) %Function
dfdeta = [y(2)
(4/beta)*((y(1))^(1/4)-1)];
end
function res = fsbc(y0,y1) %Boundaries Conditions
res = [y0(2)
-((4*fi)/beta)*(y1(1)^(1/4)-1+pac-pev)];
end
this is my code I don't know why Matlab gives me this type of error
Error using case_1>fsode
Too many input arguments.
Error in bvparguments (line 105)
testODE = ode(x1,y1,odeExtras{:});
Error in bvp4c (line 130)
bvparguments(solver_name,ode,bc,solinit,options,varargin);
Error in case_1 (line 26)
sol = bvp4c(@fsode,@fsbc,solinit);
can anyone help? thank you

Best Answer

There are three parts to this problem:
1. Error: Too many input arguments.
To solve this issue, the second argument to bvpinit should have 2 entries instead of 3. This is an initial guess for all the mesh points. The fsode function accepts the y input argument which is expected to be a 2-length vector in your case. You can read more about 'yinit' argument here: https://www.mathworks.com/help/matlab/ref/bvpinit.html#mw_1c665a1d-6f2b-438a-95eb-6c6a2cd19026
solinit = bvpinit(linspace(0,infinity,2),[25 0]);
2. Even with this change you will see an error that the defined constants are not available inside the functions.
To do that, you will have to pass them as inputs to your fsode and fsbc functions. Some examples are available here: https://www.mathworks.com/matlabcentral/answers/274406-ode45-extra-parameters#comment_351560. Some sample code is given below which you can adapt from:
sol = bvp4c(@(x,y) fsode(x,y,rsco,rje,rd,beta_,pac,pev,fi_), ...
    @(y0,y1) fsbc(y0,y1,rsco,rje,rd,beta_,pac,pev,fi_),...
    solinit);
function dfdeta = fsode(x,y,rsco,rje,rd,beta_,pac,pev,fi_) %Function 
 dfdeta = [y(2)
        (4/beta_)*((y(1))^(1/4)-1)];
end
function res = fsbc(y0,y1,rsco,rje,rd,beta_,pac,pev,fi_) %Boundaries Conditions
res = [y0(1)
      -((4*fi_)/beta_)*(y1(1)^(1/4)-1+pac-pev)];
end
3. With these changes, the script would compile but might throw warnings.
If you see the warning: Unable to meet the tolerance without using more than 5000 mesh points...
You could experiment with appropriate initial choices and boundary conditions. You can also refer to the answer here for some ideas.
Here are a couple of examples from the Docs which should help you better understand how the bvp4c and the bvpinit functions can be used:
a. Solve Second-Order BVP
b. Using bvpinit for an initial guess of BVP solution
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