INSTALL file

In order to test the package with the linear systems in the

directory 'data', the following instrunctions could be used:

1) make

2) ./babdcr<data/example1a.txt

Available testing driver files are

example1a.txt

example1b.txt

example2a.txt

example2b.txt

example3a.txt

example3b.txt

Testing driver files with the name that ends with

'a' use the subroutines BABDCR_FACT and BABDCR_SOLV,

'b' use the subroutine BABDCR_FACTSOLV.

Files WRIGHTMATR, SWFIIIMATR and RANDMATR have boundary

blocks stored after S_i and R_i blocks.

Legend:

NRWBLK= number of rows per (row)block

NBLOKS = number of (row)blocks

example1

data: WRIGHTMATR (coefficient matrix)

WRIGHTRHS (right hand side)

WRIGHTSOL (solution)

Wright example with NRWBLK=2 and NBLOKS=200.

As shown in the paper [Wright 1993], WRIGHTMATR has the

coefficient matrix as expressed in equation (13), where

NBLOKS=200 is the number of subintervals used in the

discretization and NRWBLK=2 is the dimension of the

differential system. Boundary blocks are placed in the

last block row and the right hand side is set in order

to obtain a solution with all the components equal to 1.

example2

data: SWFIIIMATR (coefficient matrix)

SWFIIIRHS (right hand side)

SWFIIISOL (solution)

Swirling flow III example with NRWBLK=6 and NBLOKS=512.

This example represents the first linear system (in BABD

form) arising from the solution of the nonlinear system

Phi(Y)=0 by means of the Newton method. The nonlinear

system describes the Mono Implicit Runge Kutta formula

applied to the Boundary Value Problem (see [Muir, Pancer,

Jackson 2003])

y1'= y2

y2'= ( y1y4-y3y2 ) / epsilon

y3'= y4

y4'= y5

y5'= y6

y6'= -( y3y6+y1y2 ) / epsilon

-1<x<1

y3( -1 )= y3( 1 )= y4( -1 )= y4( 1 )= 0

y1( -1 )= -1, y1( 1 )= 1

This ODE is taken from the family of test problems

Swirling Flow III (SWFIII) (see [Ascher, Mattheij, Russel

1995]). The initial number of subintervals is set to

NBLOKS=512 and the order of the differential system is

NRWBLK=6. As initial guess Y^(0) of the Newton method (the

r.h.s. of the considered system is -Phi(Y^(0))) we use

( Y^(0)_i )'= ( xi, 1, 0, 0, 0, 0 )

where xi= -1+ih, i= 0,...,NBLOKS and h= 2/NBLOKS.

example3:

data: RANDMATR (coefficient matrix)

RANDRHS (right hand side)

RANDSOL (solution)

random example with NRWBLK=3 and NBLOKS=10.