/*************************    Program 3.A    ****************************/
/*                                                                      */
/************************************************************************/
/* Please Note:                                                         */
/*                                                                      */
/* (1) This computer program is written by Tao Pang in conjunction with */
/*     his book, "An Introduction to Computational Physics," published  */
/*     by Cambridge University Press in 1997.                           */
/*                                                                      */
/* (2) No warranties, express or implied, are made for this program.    */
/*                                                                      */
/************************************************************************/

#include <stdio.h>
#include <math.h>

void nmrv (n,h,q,s,u)
/* The Numerov algorithm for the equation u"(x)+q(x)u(x)=s(x)
   as given in Eqs. (3.77)-(3.80) in the book.
   Copyright (c) Tao Pang 1997. */
int n;
double h;
double q[],s[],u[];
{
int i;
double g,c0,c1,c2,di,ut;

g = h*h/12;
for (i = 1; i < n-1; ++i)
  {
  c0 = 1+g*((q[i-1]-q[i+1])/2+q[i]);
  c1 = 2-g*(q[i+1]+q[i-1]+8*q[i]);
  c2 = 1+g*((q[i+1]-q[i-1])/2+q[i]);
  di = g*(s[i+1]+s[i-1]+10*s[i]);
  ut = c1*u[i]-c0*u[i-1]+di;
  u[i+1] = ut/c2;
  }
}