Hi all, (Don't mean to spam, meant to put this in General Math not General Engineering!)(adsbygoogle = window.adsbygoogle || []).push({});

I'm running the following code in MATLAB:

function M = nonNewtonian(~)

M = bvpinit(linspace(0,10,301),@VKinit);

sol = bvp4c(@VK,@VKbc,M);

figure;

hold all;

plot(sol.x,sol.y(2,;

plot(sol.x,sol.y(4,;

hold off;

xlabel('\zeta')

xlabel('\zeta')

hleg = legend('F\prime','G\prime',...

'Location','NorthEast'); %#ok<NASGU>

figure;

hold all;

plot(sol.x,sol.y(1,;

plot(sol.x,sol.y(3,;

plot(sol.x,(-1)*sol.y(5,;

hold off;

xlabel('\zeta')

hleg = legend('F','G','-H',...

'Location','East'); %#ok<NASGU>

function yprime = VK(x,y)

n=1;

yprime = [ y(2)

n^(-1)*((y(2)^(2)+y(4)^(2))^((n-1)/2))^(-1)*((y(1)^(2)-y(3)^(2)+(y(5)+((1-n)/(n+1))*y(1)*x)*y(2))*(1+(n-1)*(y(2)^(2)+y(4)^2)^(-1)*y(4)^(2))-(n-1)*y(2)*y(4)*(y(2)^(2)+y(4)^(2))^(-1)*(2*y(1)*y(3)+(y(5)+((1-n)/(n+1))*y(1)*x)*y(4)))

y(4)

n^(-1)*((y(2)^(2)+y(4)^(2))^((n-1)/2))^(-1)*((2*y(1)*y(3)+(y(5)+((1-n)/(n+1))*y(1)*x)*y(4))*(1+(n-1)*(y(2)^(2)+y(4)^2)^(-1)*y(2)^(2))-(n-1)*y(2)*y(4)*(y(2)^(2)+y(4)^(2))^(-1)*(y(1)^(2)-y(3)^(2)+(y(5)+((1-n)/(n+1))*y(1)*x)*y(2)))

-2*y(1)-(1-n)/(n+1)*x*y(2)];

function res = VKbc(ya,yb)

res = [ya(1);ya(3)-1;ya(5);yb(2)-(yb(5)*yb(1));yb(4)-(yb(5)*yb(3))];

function yinit = VKinit(~)

yinit = [0;0;1;0;0];

but receive the following error message:

??? Error using ==> bvp4c at 252

Unable to solve the collocation equations -- a singular Jacobian encountered.

Error in ==> nonNewtonian at 4

sol = bvp4c(@VK,@VKbc,M);

I struggle to see where I am going wrong?! Five differential equations and five boundary conditions, should be fine? I'm using n=1 as a test case here. I know the solutions to this system for n=1 but would like to look into the solutions when n is not equal to one.

Any help anyone could give would be greatly appreciated.

Thanks!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# MATLAB Help (BVP4C)

**Physics Forums | Science Articles, Homework Help, Discussion**