d02gbf

Purpose

Synopsis

[c,d,gam,y,np,x,ifail] = d02gbf(a,b,tol,fcnf,fcng,c,d,gam<,np,mnp,x,ifail>)

Description

 
 D02GBF solves the linear two-point boundary value problem for a 
 system of n ordinary differential equations in the interval 
 [a,b]. The system is written in the form
 
                        y'=F(x)y+g(x)                          (1)
 
 and the boundary conditions are written in the form
 
                     Cy(a)+Dy(b)=(gamma)                       (2)
 
 Here F(x), C and D are n by n matrices, and g(x) and (gamma) are 
 n-component vectors. The approximate solution to (1) and (2) is 
 found using a finite-difference method with deferred correction. 
 The algorithm is a specialisation of that used in subroutine 
 D02RAF which solves a nonlinear version of (1) and (2). 
 
 The user supplies an absolute error tolerance and may also supply
 an initial mesh for the construction of the finite-difference 
 equations (alternatively a default mesh is used). The algorithm 
 constructs a solution on a mesh defined by adding points to the 
 initial mesh. This solution is chosen so that the error is 
 everywhere less than the user's tolerance and so that the error 
 is approximately equidistributed on the final mesh. The solution 
 is returned on this final mesh.
 
 If the solution is required at a few specific points then these 
 should be included in the initial mesh. If, on the other hand, 
 the solution is required at several specific points, then the 
 user should use the interpolation routines provided in Chapter 
 E01 if these points do not themselves form a convenient mesh.
 

Parameters

d02gbf

Required Input Arguments:

a                                     real
b                                     real
tol                                   real
fcnf                                  function (User-Supplied)
fcng                                  function (User-Supplied)
c (:,:)                               real
d (:,:)                               real
gam (:)                               real

Optional Input Arguments:                       <Default>

np                                    integer  0
mnp                                   integer  2*max(np,32)
x (mnp)                               real     zeros(mnp,1)
ifail                                 integer  -1

Output Arguments:

c (:,:)                               real
d (:,:)                               real
gam (:)                               real
y (:,mnp)                             real
np                                    integer
x (mnp)                               real
ifail                                 integer