PROGON4                  Library  "JINRLIB"                      
                                       
    Author: E.V.Zemlyanaya                                           You are
    Language: Fortran                                                
                                                                     visitor here.

    SOLUTION OF THE BOUNDARY PROBLEM FOR THE ORDINARY DIFFERENTIAL EQUATION

    Subroutine PROGON4 solves the ODE in the following form

                    Z"(x)+F(x)*Z'(x)+G(x)*Z(x)=K(x)

    at the interval [a,b] with the boundary conditions:

                    D1*Z'(x=a)+F1*Z(x=a) = G1
                    D2*Z'(x=b)+F2*Z(x=b) = G2

    The generalized Numerov's method is used for the 4-th order finite difference 
    approximation. This approach was suggested and implemented in SLIPH4 [1] in the 
    framework of Newtonian scheme for numerical solution of the Sturm-Liouville problem. 
    Later, this method was generalized for the system of two ODEs in the PROGS2H4 [2].

    References:
    -----------
    1. I.V.Puzynin, T.P.Puzynina, T.A.Strizh. JINR Comm. Ð11-87-332, Dubna, 1987.
    2. E.V.Zemlyanaya, I.V.Puzynin, T.P.Puzynina. JINR Comm. P11-97-414, Dubna, 1997.

    Usage:
    ------ 
    CALL PROGON4(N,H,F,G,UK,D1,D2,F1,F2,G1,G2,Z,AV,BV), where:
       N     - (INTEGER) number of nodes of the discrete mesh;
       H     - (REAL*8) the stepsize of the discrete mesh;
               X(i)=a+(i-1)*H, i=1,...,N;
       F,G   - (REAL*8) arrays of coefficients of ODE (dimension N);
               Values F(1),F(N), G(1),G(N), UK(1),UK(N) are not needed;
       UK    - (REAL*8) array of the right part of ODE (dimension N);
       D1,D2,F1,F2,G1,G2 - (REAL*8) coefficients of the boundary conditions;
       Z     - (REAL*8) array of dimension N; calculated solution is returned;
       AV,BV - (REAL*8) working arrays (dimension N).

    Sources and description (in Russian) are submitted.