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

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SUMMARY

The discussion focuses on applying the Shooting Method to solve a system of two ordinary differential equations (ODEs) with boundary conditions (BCs). The user has attempted to use MATLAB ODE solvers but encountered issues when treating the problem as an initial value problem (IVP). The equations provided include specific derivatives for Pb and A with respect to X, which are critical for implementing the Shooting Method effectively. The user seeks guidance on correctly applying this method to achieve the desired boundary conditions.

PREREQUISITES
  • Understanding of boundary value problems (BVP) in ODEs
  • Proficiency in MATLAB for numerical solving of ODEs
  • Familiarity with the Shooting Method technique
  • Knowledge of differential equations and their applications
NEXT STEPS
  • Study the implementation of the Shooting Method in MATLAB
  • Learn about boundary value problem solvers available in MATLAB
  • Explore numerical methods for solving ODEs, focusing on BVPs
  • Review examples of applying the Shooting Method to similar ODE systems
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Students and researchers in applied mathematics, engineers dealing with differential equations, and anyone looking to solve boundary value problems using numerical methods.

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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.
 
Last edited:
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Problem solved using IVP solving procedure and shooting method
 

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