Concepts Assignment 3  
CSI 801   10/12/95

Do the following exercises in Golub & Ortega using the IMSL C library.

1.  Exercise 5.2.7, except use the fifth and sixth order Runge-Kutta
    method implemented in the IMSL function 
       void imsl_f_ode_runge_kutta (int neq, float *t, float tend,
                                float y[], void *state, void fcn())
    which solves the system y' = f(y), where y is a vector and f is a
    vector function.  The arguments are:
       int neq is the number of equations
       float *t is the independent variable (initialize it to the
                initial value)  
       float tend is the value of t at which the solution is desired
       float y[] vector of length neq of values of the dependent
                variable (initialize it to the initial values)
       char *state is a pointer to a structure that is initialized by 
                    imsl_f_ode_runge_kutta_mgr  
***             (state is shown as void * in the documentation.  It
***             would work either way on some compilers, but not on
***             SGI's.) 
           To set it up, just issue the reference
           imsl_f_ode_runge_kutta_mgr (IMSL_ODE_INITIALIZE, &state, 0)
       void fcn is the vector of functions of y' in terms of t and y:
           void fcn (int neg, float t, float *y, float *yprime)
    (The example shown in iptdoc for this function is the
     predator-prey problem, so check it out!)

2.  Exercise 5.2.17, 
      using imsl_f_ode_runge_kutta and  imsl_f_ode_adams_gear.
    The Adams-Gear routine is
       void imsl_f_ode_adams_gear (int neq, float *t, float tend,
                                float y[], void *state, void fcn())
    with the same meanings for the arguments as imsl_f_ode_runge_kutta.
    Its state is initialized by 
           imsl_f_ode_adams_gear_mgr (IMSL_ODE_INITIALIZE, &state, 0)  

3.  Exercise 5.2.18,
      using imsl_f_ode_runge_kutta and imsl_f_ode_adams_gear.