MATLAB: BVP4C: Error: Unable to solve the collocation equations — a singular Jacobian encountered

Question

Hello, I am facing "Unable to solve the collocation equations — a singular Jacobian encountered" error using BVP4C function.Below are the details:

Equations:

1–> f''' + ff'' – f'^2 + B(f''^2-ff'''')+Zg' – M^2f' + D^2 = 0

2–> Yg''+ fg' +f'g – I(2g +f'') = 0

3–> h'' +Prfh'+PrQh = 0

Boundary Conditions:

f(0)=0, f'(0)=1+Kf''(0), f'(infty)=D, f''(infty) = 0

h'(0)=-ga*(1-h(0)) , h(infty)=0

g(0)=-Mzf''

I have formulated equations & boundary conditions in m script as follows:

ff = [y(2)  
      y(3)
      y(4)
      y(5)
      (- y(1)*y(3) + y(2)^2 - B*y(3)^2 - Z* y(5)+ M^2*y(2)-D^2)
      (-y(1)*y(5)-y(2)*y(4)+I*(2*y(4)+y(3)))
      y(6)
      y(7)
      -pr * ((y(1)*y(7)) + Q*(y(6)))];
res = [ya(1)
       ya(2) - 1 - K*ya(3)
       yb(1)
       yb(2)-D
       ya(4)+Mz*ya(3) 
       yb(3)
       ya(5)
       ya(6) + ga * (1 - ya(5))
       yb(6)];

Where , y(1) = f, y(2) = f', y(3) = f'', y(4) = g, y(5) = g'',y(6) = h, y(7) = h'

All the parameters used for equation(M,I,B etc.) are known & defined as global variables.

Script is developed referring to the BVP4C samples.

Please help me resolve this error. Thanks.

Answer 1

y1'=y2
y2'=y3
y3'=y4
y4'=solve your first equation for f''''
y5'=y6
y6'=solve your second equation for g''
y7'=y8
y8'=solve your third equation for h''
(y1=f, y2=f', y3=f'', y4'=f''', y5=g, y6=g', y7=h, y8=h')

Now specify 8 boundary conditions (instead of 7 in the problem formulation or 9 in the code as above), and you are done.

Best wishes

Torsten.