Using BVP4C for overdetermined system

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In summary, the conversation discusses an overdetermined nonlinear system of ODEs with boundary conditions. The speaker mentions splitting the equations into first order ODEs and using Matlab for numerical solutions. They also mention a potential issue with using bvp4c due to too many boundary conditions and ask for alternative approaches. Finally, they realize that the problem was caused by not declaring parameters, leading to an extra dimension.
  • #1
ktsharp
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I have an overdetermined nonlinear system of ODEs:

W' = f(c)
c'' = f(W,W',c)

and boundary conditions
W(0)=a,W(L)=-a
c(0)=c(L)-b

I can split up the equations into three first order ODEs, and solve numerically with Matlab. I would like to use bvp4c, but I believe I have too many boundary conditions. Is this correct? If so, what alternative approach should I take to finding a solution. And if not, what am I doing wrong? I have already implemented the shooting method which is very sensitive on ICs for convergence, so looking for alternative method.

Regards,
 
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  • #2
I've realized that I haven't declared any parameters, and thus introduce an extra dimension. This was the problem!
 

1. What is BVP4C and how is it used for solving overdetermined systems?

BVP4C (Boundary Value Problem 4th Order Runge-Kutta) is a numerical method used for solving boundary value problems in differential equations. It is specifically designed for solving systems of differential equations that are overdetermined, meaning they have more equations than unknowns.

2. Why is BVP4C a useful tool for solving overdetermined systems?

BVP4C is a useful tool because it allows for the efficient and accurate solution of systems of differential equations with more equations than unknowns. It also takes into account the boundary conditions, making it a reliable method for solving overdetermined systems.

3. How does BVP4C handle the extra equations in an overdetermined system?

BVP4C uses a combination of the 4th order Runge-Kutta method and finite difference methods to solve the system of equations. It also adjusts the initial conditions to satisfy as many equations as possible while still satisfying the boundary conditions.

4. What are the limitations of using BVP4C for overdetermined systems?

BVP4C may not be suitable for all types of overdetermined systems, particularly those with highly non-linear equations. It also requires careful selection of initial conditions and may not always provide a unique solution.

5. Can BVP4C be used for systems with singularities or discontinuities?

Yes, BVP4C can handle systems with singularities or discontinuities by incorporating appropriate boundary conditions and handling any resulting stiffness in the equations.

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