MATLAB: How to solve a system of ODEs having coefficients in vector form using bvp4c

Question

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.

Answer 1

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