Solving Singular BVPs
bvp4c solves a class of singular BVPs of the form
It can also accommodate unknown parameters for problems of the form
Singular problems must be posed on an interval with . Use
bvpset to pass the constant matrix to
bvp4c as the value of the
'SingularTerm' integration property. Boundary conditions at must be consistent with the necessary condition for a smooth solution, . An initial guess should also satisfy this necessary condition.
When you solve a singular BVP using
bvp4c requires that your function
odefun(x,y) return only the value of the term in Equation 14-3.
Example: Solving a BVP that Has a Singular Term
Emden's equation arises in modeling a spherical body of gas. The PDE of the model is reduced by symmetry to the ODE
on an interval . The coefficient is singular at , but symmetry implies the boundary condition . With this boundary condition, the term
is well-defined as approaches 0. For the boundary condition , this BVP has the analytical solution
The demo |
bvpinitto form the guess structure
bvp4csyntax to solve the problem.
|Using Continuation to Make a Good Initial Guess||Changing BVP Integration Properties|