over an interval subject to () nonlinear boundary conditions at and () nonlinear boundary conditions at , where . Note that is the th derivative of the th solution component. Hence . The left boundary conditions at are defined as
You must specify the new initial mesh. The previous mesh can be obtained by a call to nag_ode_bvp_coll_nlin_diag (d02tzc). It may be used unchanged as the new mesh, in which case any fixed points in the previous mesh remain as fixed points in the new mesh. Fixed and other points may be added or subtracted from the mesh by manipulation of the contents of the array argument ipmesh. Initial values for the solution components on the new mesh are computed by interpolation on the values for the solution components on the previous mesh.
On entry: the number of points to be used in the new initial mesh. It is strongly recommended that if this function is called that the suggested value (see below) for nmesh is used. In this case the arrays mesh and ipmesh returned by nag_ode_bvp_coll_nlin_diag (d02tzc) can be passed to this function without any modification.
Note: the dimension, , of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument rcomm in the previous call to nag_ode_bvp_coll_nlin_solve (d02tlc).
On exit: contains information about the solution for use on subsequent calls to associated functions.
– IntegerCommunication Array
Note: the dimension, , of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument icomm in the previous call to nag_ode_bvp_coll_nlin_solve (d02tlc).
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
The first element of array mesh does not coincide with the left hand end of the range previously specified.
First element of mesh: ; left hand of the range: .
The last point of the new mesh does not coincide with the right hand end of the range previously specified.
Last point of the new mesh: ; right hand end of the range: .
The solver function does not appear to have been called.
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
Consider the problem of swirling flow over an infinite stationary disk with a magnetic field along the axis of rotation. See Ascher et al. (1988) and the references therein. After transforming from a cylindrical coordinate system , in which the component of the corresponding velocity field behaves like , the governing equations are
with boundary conditions
where is the magnetic field strength, and is the Rossby number.
Some solutions of interest are for , small and . An added complication is the infinite range, which we approximate by . We choose and first solve for using the initial approximations and , which satisfy the boundary conditions, on a uniform mesh of points. Simple continuation on the parameters and using the values and then is used to compute further solutions. We use the suggested values for nmesh, ipmesh and mesh in the call to nag_ode_bvp_coll_nlin_contin (d02txc) prior to a continuation call, that is only every second point of the preceding mesh is used.