MATLAB: How can i fix ‘Unable to solve the collocation equations — a singular jacobian encountered’ problem

boundarybvp4ccodeerrorjacobian

Our coupled equations:

f'''+(12/5)*f''*f-(4/5)*((f')^2)+q=0 q''+(12/5)*Pr*(f*q)'=0

Here is our boundary conditions:

q(0)=1 q'(0)=0 q(inf)=0

f''(0)=0 f'(inf)=0 f(0)=0 inf:infinity

Here is our function:

function dydx = fun(x,y)
 Pr=0.1;
 dydx = [ y(2)
 y(3)
 -(12/5)*(y(3))*y(1)+(4/5)*(y(2)^2)-y(4)
 y(5)
 -(12/5)*Pr*(y(4)*y(2)+y(5)*y(1))];
 end % End nested function
And boundary conditions:
 res = fun_bc(f0,finf)
   res = [ f0(1)-1
  f0(2)
  f0(3)
  f0(1)
   finf(2)];

*y(1)=f y(2)=f' y(3)=f'' y(4)=q y(5)=q' However, when we run the code we face the problem 'Unable to solve the collocation equations — a singular jacobian encountered.' How can we solve this problem?

Thanks

Best Answer

You can't prescribe f(0)=1 and f(0)=0 at the same time as boundary condition.

Best wishes

Torsten.

Related Solutions

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MATLAB: Bvp4c Error; cannot solve collocation equations- singular Jacobian

Replace

function dy=projode(n,y)
global Pr A M Ec
dy=[y(2); y(3); A*y(2)+A*n*y(3)/2+M*y(2)+y(2)^2-y(1)*y(3)-1-A-M; y(4);...
  Pr*(2*y(2)*y(4)+A*2*y(4)+A*n*y(5)/2-y(1)*y(5)-Ec*M*(1-y(2))^2-Ec*y(3)^2)];

function dy=projode(n,y)
global Pr A M Ec
dy=[y(2); y(3); A*y(2)+A*n*y(3)/2+M*y(2)+y(2)^2-y(1)*y(3)-1-A-M; y(5);...
  Pr*(2*y(2)*y(4)+A*2*y(4)+A*n*y(5)/2-y(1)*y(5)-Ec*M*(1-y(2))^2-Ec*y(3)^2)];