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How can I solve a system of ODEs having coefficients in vector form using bvp4c ?

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Tanya Sharma
Tanya Sharma on 3 Oct 2019
Commented: darova on 11 Oct 2019
Hi,
I am solving a system of 5 ODEs that contains known parameters, unknown parameters and some coefficients are of the form of vector.
%-------------------------------ODE system-----------------------------------%
function eqns = odes(x,y,e)
global Pr phi Ra Da Fr A1 A2 fdesh fdeshdesh thetadesh;
eqns = [y(2)
y(3)
(phi./Da).*y(2)+(2.*phi.*Fr./A1).*fdesh.*y(2)-(fdesh.*1./A1).*y(3)-(fdeshdesh.*1./A1).*y(1)+(2.*fdesh.*1./A1).*y(2)-(e./A1).*y(2)-(phi.*Ra./(A1^2).*A2).*y(4)
y(5)
-(Pr./A2).*(fdesh.*y(5)+thetadesh.*y(1)+e.*y(4))];
end
%------------------------------------------------------------------------------------------------
--------------------% fdesh, fdeshdesh and thetadesh are of vector form. these are the known solution of the governing equations .%----------------------
%----------------------------------------------------------------------------------------------
%--------------------------boundary conditions-----------------------------%
function res = ode_bc(ya,yb,e)
res = [ya(1)
ya(2)
ya(3)
ya(4)
yb(2)
yb(4)];
end
%-------------------------------------------------------------------------------------------------
I am getting this error:
Error using bvparguments (line 108)
Error in calling BVP4C(ODEFUN,BCFUN,SOLINIT):
The derivative function ODEFUN should return a column vector of length 5.
%-------------------------------------------------------------------------------------------------------
are the known solutions causing a problem to solve the system?
Thanks in advance.

Accepted Answer

darova
darova on 3 Oct 2019
Try this
function eqns = odes(x,y,e,x0)
global Pr phi Ra Da Fr A1 A2 fdesh fdeshdesh thetadesh; % global variables are not recommended
% x0 - vector of corresponding values for fdesh, fdeshdesh, thetadesh
% x0(end) should not be bigger than x(end)
fd = interp1(x0,fdesh,x);
fdd = interp1(x0,fdeshdesh,x);
thd = interp1(x0,thetadesh,x);
eqns = [y(2)
y(3)
(phi./Da).*y(2)+(2.*phi.*Fr./A1).*fd.*y(2)-(fd.*1./A1).*y(3)-(fdd.*1./A1).*y(1)+(2.*fd.*1./A1).*y(2)-(e./A1).*y(2)-(phi.*Ra./(A1^2).*A2).*y(4)
y(5)
-(Pr./A2).*(fd.*y(5)+thd.*y(1)+e.*y(4))];
end
  10 Comments
darova
darova on 9 Oct 2019
I don't think β patameter can be found. In the paper you attached everywhere is said that it can be obtained with guess

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More Answers (1)

Tanya Sharma
Tanya Sharma on 10 Oct 2019
Yes and the guess is provided in the "solinit" structure as an extra parameter
beta = 99;
init2 = bvpinit(linspace(-1,1,50),@math4init,beta);
Which we can later be obtain by "sol.parameters", this provides us the value bvp4c has taken nearer to our provided guess.
Which in this case is:
beta=77.8263.
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