#*****************************************************************************80
#
## bvpexample_test tests bvpexample.
#
#  Licensing:
#
#    Copyright 2016 James P. Howard, II
#
#    The computer code and data files on this web page are distributed under
#    https://opensource.org/licenses/BSD-2-Clause, the BSD-2-Clause license.
#
#  Modified:
#
#    28 March 2020
#
#  Author:
#
#    John Burkardt
#
cat ( date ( ), "\n" )
cat ( "\n" )
cat ( "bvpexample_test\n" )
cat ( " ", version$version.string, "\n" )
cat ( "  bvpexample determines the additional initial value which\n" )
cat ( "  converts a boundary value problem (BVP) into\n" )
cat ( "  an initial value problem (IVP).\n" )
cat ( "\n" )

source ( "/home/burkardt/public_html/r_src/bisection/bisection.R" )  
source ( "/home/burkardt/public_html/r_src/bvpexample/bvpexample.R" )  
#
#  Initial exploration shows that the correct value is between 0 and 1.
#
for ( b in -2 : 2 )
{
  value = bvpexample ( b )
  cat ( "  f(", b, ") = ", value, "\n" )
}
#
#  Call bisection to get the correct value.
#
bvp.b <- bisection ( bvpexample, 0.0, 1.0 )
cat ( "\n" )
cat ( "  Correct initial value for y'(0) is ", bvp.b, "\n" )
#
#  Solve IVP with additional initial value.
#
odesystem <- function ( x, y )
{
  y1 <- y[2]
  y2 <- y[1]^2 - 2.0
  return ( c ( y1 = y1, y2 = y2 ) )
}
x0 <- 0.0
y0 <- c ( y1 = 1.0, y2 = bvp.b )
yn <- 1.0
n <- 1000
h <- 1.0 / n
z <- eulersys ( odesystem, x0, y0, h, n )
print ( tail ( z, 1 ) )
#
#  Terminate.
#
cat ( "\n" )
cat ( "bvpexample_test\n" )
cat ( "  Normal end of execution.\n" )
cat ( date ( ), "\n" )

quit ( )