How to Apply the Shooting Method to a System of ODEs with Boundary Conditions?

[k.dineshkumar]

Homework Statement

I have a problem in solving a system of two ODEs for BVP

1. Pb is function of X & A
2. A is a function of X,Pb,A
3. BCs are
X = 1, Pb = 0, A = 0.441
X = 0, Pb = 0
Q is a variable to achieve the other end BC
I have tried to use ODE solvers in matlab. But I couldn't get proper results by considering it as IVP.

Homework Equations

dPbdX = (-(1.6+0.2*X^2)/(1.6+0.4*X^2)*(sqrt(3)*(1-A)^2)-Q)*(0.3/(sqrt(3)*(sqrt(3)*(1-A)^2)^2))
dAdX = (0.4*X*(((2-(1-A)*Pb)/A)-Pb)*(-0.86*A^2+0.345*A+0.515))/((0.08+0.02*X^2)*(2-(((2-(1-A)*Pb)/A)-Pb)*(1/(2.571-A-A*ln(1-A)))))

How to use Shooting method for this problem?

I would appreciate for giving me a helping hand to solve this problem.

 

[k.dineshkumar]

Problem solved using IVP solving procedure and shooting method