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

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In summary, the conversation discusses a problem in solving a system of two ODEs for BVP, where Pb is a function of X and A, A is a function of X, Pb, and A, and BCs are given at two points. The conversation also mentions using ODE solvers in Matlab, but not getting proper results, and considering the problem as an IVP. It then asks about using the Shooting method and asks for help in solving the problem. The problem is later solved using IVP solving procedure and the Shooting method.
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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.
 
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Problem solved using IVP solving procedure and shooting method
 

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

What is a BVP for a system of ODEs?

A BVP (boundary value problem) for a system of ODEs (ordinary differential equations) is a type of mathematical problem where the values of the solution are known at the boundaries of the domain, and the goal is to find the solution within that domain that satisfies the given boundary conditions.

Why is help needed for solving BVPs for systems of ODEs?

Solving BVPs for systems of ODEs can be a complex and time-consuming task, requiring advanced mathematical knowledge and specialized software. Additionally, the specific boundary conditions and system of equations can vary greatly, making it difficult to find a general solution method.

What are some common techniques for solving BVPs for systems of ODEs?

Some common techniques for solving BVPs for systems of ODEs include finite difference methods, shooting methods, and collocation methods. These methods involve discretizing the domain and/or equations, and then using numerical algorithms to approximate the solution.

Can BVPs for systems of ODEs be solved analytically?

In most cases, BVPs for systems of ODEs cannot be solved analytically. However, in some special cases where the equations and boundary conditions are simple enough, analytical solutions may be possible.

How can I get help with solving a BVP for a system of ODEs?

If you are struggling with solving a BVP for a system of ODEs, you can seek help from a math tutor or consult online resources and forums. You can also reach out to colleagues or experts in the field for guidance and assistance.

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