I need to solve system of two equations with bvp4c method, where p is the pressure and it is only function of longitudinal coordinate z. It means p = f(z) and dpdz is the first derivative of p:
p0' = - 32 .* beta .* m0 ./ (R .^ 4 .* p0)
p1' = - ( - 8 .* p0' ./ R - p0' .* p1 - 32 .* beta .* m1 ./ R .^ 4 ) ./ p0
I defined it in Matlab function file bvpfcn.m with neccessary constants, where I want to have solution of every equation in 1001 points, it means 1x1001 is dimension of z. Exactly I need that z is going from 0 to 1 with 1001 points between 0 and 1, but I dont know where to write that:
function dpdz = bvpfcn(z,p)
beta = 1;
m0 = 1;
m1 = 0.1;
ri = 0.7;
R = ri - z .* (ri - 1);
dpdz = zeros(2,1001);
dpdz = [- 32 .* beta .* m0 ./ (R .^ 4 .* p(1))
-( - 8 .* dpdz(1) ./ R - dpdz(1) .* p(2) - 32 .* beta .* m1 ./ R .^ 4 ) ./ p(1);
];
end
I have initial conditions where p(1) = p0 and p(2) = p1, and conditions are
p(1)|(z=0) = 8
p(1)|(z=1) = 1
p(2)|(z=0) = 0
p(2)|(z=1) = 0
which I defined if function file bcfcn.m, where pa are values of p at z=0, and pb are values of p at z=1. So boundary conditions are given as [[p0[0] p1[0]] [p0[1] p1[1]]]:
function res = bcfcn(pa,pb)
res = [[pa(1)-8 pa(1) ]
[pb(1)-1 pb(1) ]];
end
My solution need to be of shape:
Because of that I am making guess function of cosine type, I am not sure is this good assumption?
function g = guess(z)
g = [cos(z)
cos(z)];
end
And call all with code:
clear all;
beta = 1;
m0 = 1;
m1 = 0.1;
ri = 0.7;
xmesh = linspace(0,pi/2,1001);
solinit = bvpinit(xmesh, @guess);
sol = bvp4c(@bvpfcn, @bcfcn, solinit);
This is error which I got:
In an assignment A(:) = B, the number of elements in A and B must be the same.
Error in bvp4c>colloc_RHS (line 600)
Phi(1:nBCs) = Gbc(y(:,Lidx),y(:,Ridx),ExtraArgs{1:nExtraArgs});
Error in bvp4c (line 189)
[RHS,yp,Fmid,NF] = colloc_RHS(n,x,Y,ode,bc,npar,xyVectorized,mbcidx,nExtraArgs,ExtraArgs);
