*************************************************************************
*                                                                       *
*        Tina Bosner                                                    *                
*                                                                       *
*        Doctoral Thesis:                                               *
*        "Knot insertion algorithms for Chebyshev splines"              *
*                                                                       *
*************************************************************************

This CD is an appendix of the doctoral thesis, and contains the routines 
for calculating with tension splines. For practical use of this routines,
two examples are presented. Both of the examples solves the same 
singularly perturbed differential two-point boundary value problem:

ey"+y'-(1+e)*y=0, y(0)=1+exp(-1), y(1)=1+exp(-(1+e)/e, e<<1

by the collocation method by C^1 tension splines in the first example, 
and by C^2 tension splines in the second. This two examples are divided in
two directories, each containing all necessary routines (some of the 
routines are repeated in both directories). They also uses IMSL library,
more specific, the subroutines DLSARB and DLSLTR for solving a system of 
linear equations, as well as the program GNUPLOT for plotting the results
(for download of GNUPLOT use www.gnuplot.info/download.html).   

******************************
Directory "TensionSplinesC1"
******************************

The project for solving the Example 8.1 contains:
the main program:   
                  exampleC1.f90 
the routines for solving singularly perturbed differential two-point 
boundary value problem by the collocation method by C^1 tension splines at 
the generalized Gaussian points:
     module:      examplediffeqC1.f90
     subroutines: linsystemC1.f90
                  diffopC1.f90 
     function:    gausspoints.f90
the routines for calculating with C^1 tension splines:
     module:      functions.f90
     subroutines: tension4C1.f90
                  tension3C1.f90
                  tension2.f90
                  tension1der4C1.f90
                  tension2der4C1.f90
                  tension1der4C1coeff.f90
                  tension1der3C1coeff.f90
the GNUPLOT script (the instructions for plotting in GNUPLOT):
                  plotC1.txt

******************************
Directory "TensionSplinesC2"
******************************

The project for solving the Example 8.2 contains:
the main program:   
                  exampleC2.f90 
the routines for solving singularly perturbed differential two-point 
boundary value problem by the collocation method by C^2 tension splines at
the knots of the partition:
     module:      examplediffeqC2.f90
     subroutines: linsystemC2.f90
                  diffopC2.f90 
the routines for calculating with C^2 tension splines:
     module:      functions.f90
     subroutines: tension4C2.f90
                  tension4C1.f90
                  tension3C2.f90
                  tension3C1.f90
                  tension2.f90
                  tension1der4C2.f90
                  tension2der4C2.f90
                  tension1der4C2coeff.f90
                  tension1der3C2coeff.f90
the GNUPLOT script (the instructions for plotting in GNUPLOT):
                  plotC2.txt