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#### PROGON4 - solution of the boundary problem for the ordinary differential equation

Author: E.V.Zemlyanaya You are visitor here.  Language: Fortran

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  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 .

References:

1. I.V.Puzynin, T.P.Puzynina, T.A.Strizh. JINR Comm. Р11-87-332, 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.      