NAG Library Manual, Mark 29.3
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NAG AD Library Introduction
Example description

 D03RA_P0W_F Example Program Results

 Example 1

 Solution at every 4th grid point in level         1 at time   0.2400:

       x          y        approx u

  0.0000E+00   0.000E+00   1.985E+00
  1.0000E-01   0.000E+00   1.985E+00
  2.0000E-01   0.000E+00   1.984E+00
  3.0000E-01   0.000E+00   1.980E+00
  4.0000E-01   0.000E+00   1.948E+00
  5.0000E-01   0.000E+00   1.716E+00
  6.0000E-01   0.000E+00   1.432E+00
  7.0000E-01   0.000E+00   1.275E+00
  8.0000E-01   0.000E+00   1.169E+00
  9.0000E-01   0.000E+00   1.084E+00
  1.0000E+00   0.000E+00   1.000E+00
  7.5000E-02   2.500E-02   1.985E+00
  1.7500E-01   2.500E-02   1.985E+00
  2.7500E-01   2.500E-02   1.982E+00
  3.7500E-01   2.500E-02   1.963E+00
  4.7500E-01   2.500E-02   1.802E+00
  5.7500E-01   2.500E-02   1.487E+00
  6.7500E-01   2.500E-02   1.307E+00
  7.7500E-01   2.500E-02   1.193E+00
  8.7500E-01   2.500E-02   1.105E+00
  9.7500E-01   2.500E-02   1.022E+00
  5.0000E-02   5.000E-02   1.985E+00
  1.5000E-01   5.000E-02   1.985E+00
  2.5000E-01   5.000E-02   1.983E+00
  3.5000E-01   5.000E-02   1.972E+00
  4.5000E-01   5.000E-02   1.873E+00
  5.5000E-01   5.000E-02   1.552E+00
  6.5000E-01   5.000E-02   1.344E+00
  7.5000E-01   5.000E-02   1.218E+00
  8.5000E-01   5.000E-02   1.125E+00
  9.5000E-01   5.000E-02   1.043E+00
  2.5000E-02   7.500E-02   1.985E+00
  1.2500E-01   7.500E-02   1.985E+00
  2.2500E-01   7.500E-02   1.984E+00
  3.2500E-01   7.500E-02   1.977E+00
  4.2500E-01   7.500E-02   1.920E+00
  5.2500E-01   7.500E-02   1.629E+00
  6.2500E-01   7.500E-02   1.385E+00
  7.2500E-01   7.500E-02   1.245E+00
  8.2500E-01   7.500E-02   1.147E+00
  9.2500E-01   7.500E-02   1.064E+00
  0.0000E+00   1.000E-01   1.985E+00
  1.0000E-01   1.000E-01   1.985E+00
  2.0000E-01   1.000E-01   1.984E+00
  3.0000E-01   1.000E-01   1.980E+00
  4.0000E-01   1.000E-01   1.948E+00
  5.0000E-01   1.000E-01   1.715E+00
  6.0000E-01   1.000E-01   1.432E+00
  7.0000E-01   1.000E-01   1.275E+00
  8.0000E-01   1.000E-01   1.169E+00
  9.0000E-01   1.000E-01   1.084E+00
  1.0000E+00   1.000E-01   1.000E+00
  7.5000E-02   1.250E-01   1.985E+00
  1.7500E-01   1.250E-01   1.984E+00
  2.7500E-01   1.250E-01   1.982E+00
  3.7500E-01   1.250E-01   1.963E+00
  4.7500E-01   1.250E-01   1.801E+00
  5.7500E-01   1.250E-01   1.487E+00
  6.7500E-01   1.250E-01   1.307E+00
  7.7500E-01   1.250E-01   1.193E+00
  8.7500E-01   1.250E-01   1.105E+00
  9.7500E-01   1.250E-01   1.022E+00
  5.0000E-02   1.500E-01   1.985E+00
  1.5000E-01   1.500E-01   1.985E+00
  2.5000E-01   1.500E-01   1.983E+00
  3.5000E-01   1.500E-01   1.971E+00
  4.5000E-01   1.500E-01   1.872E+00
  5.5000E-01   1.500E-01   1.552E+00
  6.5000E-01   1.500E-01   1.344E+00
  7.5000E-01   1.500E-01   1.218E+00
  8.5000E-01   1.500E-01   1.125E+00
  9.5000E-01   1.500E-01   1.043E+00
  2.5000E-02   1.750E-01   1.985E+00
  1.2500E-01   1.750E-01   1.984E+00
  2.2500E-01   1.750E-01   1.983E+00
  3.2500E-01   1.750E-01   1.976E+00
  4.2500E-01   1.750E-01   1.918E+00
  5.2500E-01   1.750E-01   1.627E+00
  6.2500E-01   1.750E-01   1.384E+00
  7.2500E-01   1.750E-01   1.245E+00
  8.2500E-01   1.750E-01   1.147E+00
  9.2500E-01   1.750E-01   1.064E+00
  0.0000E+00   2.000E-01   1.984E+00
  1.0000E-01   2.000E-01   1.984E+00
  2.0000E-01   2.000E-01   1.983E+00
  3.0000E-01   2.000E-01   1.979E+00
  4.0000E-01   2.000E-01   1.945E+00
  5.0000E-01   2.000E-01   1.712E+00
  6.0000E-01   2.000E-01   1.431E+00
  7.0000E-01   2.000E-01   1.275E+00
  8.0000E-01   2.000E-01   1.169E+00
  9.0000E-01   2.000E-01   1.084E+00
  1.0000E+00   2.000E-01   1.000E+00
  7.5000E-02   2.250E-01   1.984E+00
  1.7500E-01   2.250E-01   1.983E+00
  2.7500E-01   2.250E-01   1.980E+00
  3.7500E-01   2.250E-01   1.960E+00
  4.7500E-01   2.250E-01   1.796E+00
  5.7500E-01   2.250E-01   1.485E+00
  6.7500E-01   2.250E-01   1.307E+00
  7.7500E-01   2.250E-01   1.193E+00
  8.7500E-01   2.250E-01   1.105E+00
  9.7500E-01   2.250E-01   1.022E+00
  5.0000E-02   2.500E-01   1.983E+00
  1.5000E-01   2.500E-01   1.983E+00
  2.5000E-01   2.500E-01   1.980E+00
  3.5000E-01   2.500E-01   1.968E+00
  4.5000E-01   2.500E-01   1.864E+00
  5.5000E-01   2.500E-01   1.549E+00
  6.5000E-01   2.500E-01   1.343E+00
  7.5000E-01   2.500E-01   1.218E+00
  8.5000E-01   2.500E-01   1.125E+00
  9.5000E-01   2.500E-01   1.043E+00
  2.5000E-02   2.750E-01   1.982E+00
  1.2500E-01   2.750E-01   1.982E+00
  2.2500E-01   2.750E-01   1.980E+00
  3.2500E-01   2.750E-01   1.972E+00
  4.2500E-01   2.750E-01   1.908E+00
  5.2500E-01   2.750E-01   1.621E+00
  6.2500E-01   2.750E-01   1.383E+00
  7.2500E-01   2.750E-01   1.245E+00
  8.2500E-01   2.750E-01   1.147E+00
  9.2500E-01   2.750E-01   1.064E+00
  0.0000E+00   3.000E-01   1.980E+00
  1.0000E-01   3.000E-01   1.980E+00
  2.0000E-01   3.000E-01   1.979E+00
  3.0000E-01   3.000E-01   1.973E+00
  4.0000E-01   3.000E-01   1.934E+00
  5.0000E-01   3.000E-01   1.698E+00
  6.0000E-01   3.000E-01   1.428E+00
  7.0000E-01   3.000E-01   1.274E+00
  8.0000E-01   3.000E-01   1.169E+00
  9.0000E-01   3.000E-01   1.084E+00
  1.0000E+00   3.000E-01   1.000E+00
  7.5000E-02   3.250E-01   1.977E+00
  1.7500E-01   3.250E-01   1.976E+00
  2.7500E-01   3.250E-01   1.972E+00
  3.7500E-01   3.250E-01   1.946E+00
  4.7500E-01   3.250E-01   1.771E+00
  5.7500E-01   3.250E-01   1.479E+00
  6.7500E-01   3.250E-01   1.306E+00
  7.7500E-01   3.250E-01   1.193E+00
  8.7500E-01   3.250E-01   1.104E+00
  9.7500E-01   3.250E-01   1.022E+00
  5.0000E-02   3.500E-01   1.972E+00
  1.5000E-01   3.500E-01   1.971E+00
  2.5000E-01   3.500E-01   1.968E+00
  3.5000E-01   3.500E-01   1.949E+00
  4.5000E-01   3.500E-01   1.827E+00
  5.5000E-01   3.500E-01   1.535E+00
  6.5000E-01   3.500E-01   1.340E+00
  7.5000E-01   3.500E-01   1.217E+00
  8.5000E-01   3.500E-01   1.125E+00
  9.5000E-01   3.500E-01   1.043E+00
  2.5000E-02   3.750E-01   1.963E+00
  1.2500E-01   3.750E-01   1.963E+00
  2.2500E-01   3.750E-01   1.960E+00
  3.2500E-01   3.750E-01   1.946E+00
  4.2500E-01   3.750E-01   1.860E+00
  5.2500E-01   3.750E-01   1.594E+00
  6.2500E-01   3.750E-01   1.378E+00
  7.2500E-01   3.750E-01   1.244E+00
  8.2500E-01   3.750E-01   1.146E+00
  9.2500E-01   3.750E-01   1.064E+00
  0.0000E+00   4.000E-01   1.948E+00
  1.0000E-01   4.000E-01   1.947E+00
  2.0000E-01   4.000E-01   1.945E+00
  3.0000E-01   4.000E-01   1.934E+00
  4.0000E-01   4.000E-01   1.870E+00
  5.0000E-01   4.000E-01   1.647E+00
  6.0000E-01   4.000E-01   1.417E+00
  7.0000E-01   4.000E-01   1.271E+00
  8.0000E-01   4.000E-01   1.168E+00
  9.0000E-01   4.000E-01   1.084E+00
  1.0000E+00   4.000E-01   1.000E+00
  7.5000E-02   4.250E-01   1.920E+00
  1.7500E-01   4.250E-01   1.918E+00
  2.7500E-01   4.250E-01   1.908E+00
  3.7500E-01   4.250E-01   1.860E+00
  4.7500E-01   4.250E-01   1.685E+00
  5.7500E-01   4.250E-01   1.457E+00
  6.7500E-01   4.250E-01   1.300E+00
  7.7500E-01   4.250E-01   1.191E+00
  8.7500E-01   4.250E-01   1.104E+00
  9.7500E-01   4.250E-01   1.022E+00
  5.0000E-02   4.500E-01   1.873E+00
  1.5000E-01   4.500E-01   1.871E+00
  2.5000E-01   4.500E-01   1.864E+00
  3.5000E-01   4.500E-01   1.827E+00
  4.5000E-01   4.500E-01   1.699E+00
  5.5000E-01   4.500E-01   1.493E+00
  6.5000E-01   4.500E-01   1.330E+00
  7.5000E-01   4.500E-01   1.215E+00
  8.5000E-01   4.500E-01   1.124E+00
  9.5000E-01   4.500E-01   1.043E+00
  2.5000E-02   4.750E-01   1.802E+00
  1.2500E-01   4.750E-01   1.801E+00
  2.2500E-01   4.750E-01   1.796E+00
  3.2500E-01   4.750E-01   1.771E+00
  4.2500E-01   4.750E-01   1.685E+00
  5.2500E-01   4.750E-01   1.519E+00
  6.2500E-01   4.750E-01   1.359E+00
  7.2500E-01   4.750E-01   1.238E+00
  8.2500E-01   4.750E-01   1.145E+00
  9.2500E-01   4.750E-01   1.063E+00
  0.0000E+00   5.000E-01   1.715E+00
  1.0000E-01   5.000E-01   1.715E+00
  2.0000E-01   5.000E-01   1.712E+00
  3.0000E-01   5.000E-01   1.698E+00
  4.0000E-01   5.000E-01   1.647E+00
  5.0000E-01   5.000E-01   1.529E+00
  6.0000E-01   5.000E-01   1.384E+00
  7.0000E-01   5.000E-01   1.262E+00
  8.0000E-01   5.000E-01   1.166E+00
  9.0000E-01   5.000E-01   1.083E+00
  1.0000E+00   5.000E-01   1.000E+00
  7.5000E-02   5.250E-01   1.629E+00
  1.7500E-01   5.250E-01   1.627E+00
  2.7500E-01   5.250E-01   1.621E+00
  3.7500E-01   5.250E-01   1.594E+00
  4.7500E-01   5.250E-01   1.519E+00
  5.7500E-01   5.250E-01   1.401E+00
  6.7500E-01   5.250E-01   1.284E+00
  7.7500E-01   5.250E-01   1.186E+00
  8.7500E-01   5.250E-01   1.102E+00
  9.7500E-01   5.250E-01   1.022E+00
  5.0000E-02   5.500E-01   1.552E+00
  1.5000E-01   5.500E-01   1.552E+00
  2.5000E-01   5.500E-01   1.549E+00
  3.5000E-01   5.500E-01   1.535E+00
  4.5000E-01   5.500E-01   1.493E+00
  5.5000E-01   5.500E-01   1.407E+00
  6.5000E-01   5.500E-01   1.302E+00
  7.5000E-01   5.500E-01   1.206E+00
  8.5000E-01   5.500E-01   1.121E+00
  9.5000E-01   5.500E-01   1.042E+00
  2.5000E-02   5.750E-01   1.487E+00
  1.2500E-01   5.750E-01   1.487E+00
  2.2500E-01   5.750E-01   1.485E+00
  3.2500E-01   5.750E-01   1.479E+00
  4.2500E-01   5.750E-01   1.457E+00
  5.2500E-01   5.750E-01   1.401E+00
  6.2500E-01   5.750E-01   1.315E+00
  7.2500E-01   5.750E-01   1.223E+00
  8.2500E-01   5.750E-01   1.140E+00
  9.2500E-01   5.750E-01   1.062E+00
  0.0000E+00   6.000E-01   1.432E+00
  1.0000E-01   6.000E-01   1.432E+00
  2.0000E-01   6.000E-01   1.431E+00
  3.0000E-01   6.000E-01   1.428E+00
  4.0000E-01   6.000E-01   1.417E+00
  5.0000E-01   6.000E-01   1.384E+00
  6.0000E-01   6.000E-01   1.319E+00
  7.0000E-01   6.000E-01   1.238E+00
  8.0000E-01   6.000E-01   1.157E+00
  9.0000E-01   6.000E-01   1.080E+00
  1.0000E+00   6.000E-01   1.000E+00
  7.5000E-02   6.250E-01   1.385E+00
  1.7500E-01   6.250E-01   1.384E+00
  2.7500E-01   6.250E-01   1.383E+00
  3.7500E-01   6.250E-01   1.378E+00
  4.7500E-01   6.250E-01   1.359E+00
  5.7500E-01   6.250E-01   1.315E+00
  6.7500E-01   6.250E-01   1.248E+00
  7.7500E-01   6.250E-01   1.172E+00
  8.7500E-01   6.250E-01   1.098E+00
  9.7500E-01   6.250E-01   1.021E+00
  5.0000E-02   6.500E-01   1.344E+00
  1.5000E-01   6.500E-01   1.343E+00
  2.5000E-01   6.500E-01   1.343E+00
  3.5000E-01   6.500E-01   1.340E+00
  4.5000E-01   6.500E-01   1.330E+00
  5.5000E-01   6.500E-01   1.302E+00
  6.5000E-01   6.500E-01   1.251E+00
  7.5000E-01   6.500E-01   1.184E+00
  8.5000E-01   6.500E-01   1.114E+00
  9.5000E-01   6.500E-01   1.040E+00
  2.5000E-02   6.750E-01   1.307E+00
  1.2500E-01   6.750E-01   1.307E+00
  2.2500E-01   6.750E-01   1.307E+00
  3.2500E-01   6.750E-01   1.306E+00
  4.2500E-01   6.750E-01   1.300E+00
  5.2500E-01   6.750E-01   1.284E+00
  6.2500E-01   6.750E-01   1.248E+00
  7.2500E-01   6.750E-01   1.192E+00
  8.2500E-01   6.750E-01   1.127E+00
  9.2500E-01   6.750E-01   1.058E+00
  0.0000E+00   7.000E-01   1.275E+00
  1.0000E-01   7.000E-01   1.275E+00
  2.0000E-01   7.000E-01   1.275E+00
  3.0000E-01   7.000E-01   1.274E+00
  4.0000E-01   7.000E-01   1.271E+00
  5.0000E-01   7.000E-01   1.262E+00
  6.0000E-01   7.000E-01   1.238E+00
  7.0000E-01   7.000E-01   1.195E+00
  8.0000E-01   7.000E-01   1.138E+00
  9.0000E-01   7.000E-01   1.074E+00
  1.0000E+00   7.000E-01   1.000E+00
  7.5000E-02   7.250E-01   1.245E+00
  1.7500E-01   7.250E-01   1.245E+00
  2.7500E-01   7.250E-01   1.245E+00
  3.7500E-01   7.250E-01   1.244E+00
  4.7500E-01   7.250E-01   1.238E+00
  5.7500E-01   7.250E-01   1.223E+00
  6.7500E-01   7.250E-01   1.192E+00
  7.7500E-01   7.250E-01   1.145E+00
  8.7500E-01   7.250E-01   1.087E+00
  9.7500E-01   7.250E-01   1.019E+00
  5.0000E-02   7.500E-01   1.218E+00
  1.5000E-01   7.500E-01   1.218E+00
  2.5000E-01   7.500E-01   1.218E+00
  3.5000E-01   7.500E-01   1.217E+00
  4.5000E-01   7.500E-01   1.215E+00
  5.5000E-01   7.500E-01   1.206E+00
  6.5000E-01   7.500E-01   1.184E+00
  7.5000E-01   7.500E-01   1.147E+00
  8.5000E-01   7.500E-01   1.097E+00
  9.5000E-01   7.500E-01   1.036E+00
  2.5000E-02   7.750E-01   1.193E+00
  1.2500E-01   7.750E-01   1.193E+00
  2.2500E-01   7.750E-01   1.193E+00
  3.2500E-01   7.750E-01   1.193E+00
  4.2500E-01   7.750E-01   1.191E+00
  5.2500E-01   7.750E-01   1.186E+00
  6.2500E-01   7.750E-01   1.172E+00
  7.2500E-01   7.750E-01   1.145E+00
  8.2500E-01   7.750E-01   1.103E+00
  9.2500E-01   7.750E-01   1.050E+00
  0.0000E+00   8.000E-01   1.169E+00
  1.0000E-01   8.000E-01   1.169E+00
  2.0000E-01   8.000E-01   1.169E+00
  3.0000E-01   8.000E-01   1.169E+00
  4.0000E-01   8.000E-01   1.168E+00
  5.0000E-01   8.000E-01   1.166E+00
  6.0000E-01   8.000E-01   1.157E+00
  7.0000E-01   8.000E-01   1.138E+00
  8.0000E-01   8.000E-01   1.106E+00
  9.0000E-01   8.000E-01   1.060E+00
  1.0000E+00   8.000E-01   1.000E+00
  7.5000E-02   8.250E-01   1.147E+00
  1.7500E-01   8.250E-01   1.147E+00
  2.7500E-01   8.250E-01   1.147E+00
  3.7500E-01   8.250E-01   1.146E+00
  4.7500E-01   8.250E-01   1.145E+00
  5.7500E-01   8.250E-01   1.140E+00
  6.7500E-01   8.250E-01   1.127E+00
  7.7500E-01   8.250E-01   1.103E+00
  8.7500E-01   8.250E-01   1.067E+00
  9.7500E-01   8.250E-01   1.016E+00
  5.0000E-02   8.500E-01   1.125E+00
  1.5000E-01   8.500E-01   1.125E+00
  2.5000E-01   8.500E-01   1.125E+00
  3.5000E-01   8.500E-01   1.125E+00
  4.5000E-01   8.500E-01   1.124E+00
  5.5000E-01   8.500E-01   1.121E+00
  6.5000E-01   8.500E-01   1.114E+00
  7.5000E-01   8.500E-01   1.097E+00
  8.5000E-01   8.500E-01   1.069E+00
  9.5000E-01   8.500E-01   1.027E+00
  2.5000E-02   8.750E-01   1.105E+00
  1.2500E-01   8.750E-01   1.105E+00
  2.2500E-01   8.750E-01   1.105E+00
  3.2500E-01   8.750E-01   1.104E+00
  4.2500E-01   8.750E-01   1.104E+00
  5.2500E-01   8.750E-01   1.102E+00
  6.2500E-01   8.750E-01   1.098E+00
  7.2500E-01   8.750E-01   1.087E+00
  8.2500E-01   8.750E-01   1.067E+00
  9.2500E-01   8.750E-01   1.034E+00
  0.0000E+00   9.000E-01   1.084E+00
  1.0000E-01   9.000E-01   1.084E+00
  2.0000E-01   9.000E-01   1.084E+00
  3.0000E-01   9.000E-01   1.084E+00
  4.0000E-01   9.000E-01   1.084E+00
  5.0000E-01   9.000E-01   1.083E+00
  6.0000E-01   9.000E-01   1.080E+00
  7.0000E-01   9.000E-01   1.074E+00
  8.0000E-01   9.000E-01   1.060E+00
  9.0000E-01   9.000E-01   1.037E+00
  1.0000E+00   9.000E-01   1.000E+00
  7.5000E-02   9.250E-01   1.064E+00
  1.7500E-01   9.250E-01   1.064E+00
  2.7500E-01   9.250E-01   1.064E+00
  3.7500E-01   9.250E-01   1.064E+00
  4.7500E-01   9.250E-01   1.063E+00
  5.7500E-01   9.250E-01   1.062E+00
  6.7500E-01   9.250E-01   1.058E+00
  7.7500E-01   9.250E-01   1.050E+00
  8.7500E-01   9.250E-01   1.034E+00
  9.7500E-01   9.250E-01   1.009E+00
  5.0000E-02   9.500E-01   1.043E+00
  1.5000E-01   9.500E-01   1.043E+00
  2.5000E-01   9.500E-01   1.043E+00
  3.5000E-01   9.500E-01   1.043E+00
  4.5000E-01   9.500E-01   1.043E+00
  5.5000E-01   9.500E-01   1.042E+00
  6.5000E-01   9.500E-01   1.040E+00
  7.5000E-01   9.500E-01   1.036E+00
  8.5000E-01   9.500E-01   1.027E+00
  9.5000E-01   9.500E-01   1.012E+00
  2.5000E-02   9.750E-01   1.022E+00
  1.2500E-01   9.750E-01   1.022E+00
  2.2500E-01   9.750E-01   1.022E+00
  3.2500E-01   9.750E-01   1.022E+00
  4.2500E-01   9.750E-01   1.022E+00
  5.2500E-01   9.750E-01   1.022E+00
  6.2500E-01   9.750E-01   1.021E+00
  7.2500E-01   9.750E-01   1.019E+00
  8.2500E-01   9.750E-01   1.016E+00
  9.2500E-01   9.750E-01   1.009E+00
  0.0000E+00   1.000E+00   1.000E+00
  1.0000E-01   1.000E+00   1.000E+00
  2.0000E-01   1.000E+00   1.000E+00
  3.0000E-01   1.000E+00   1.000E+00
  4.0000E-01   1.000E+00   1.000E+00
  5.0000E-01   1.000E+00   1.000E+00
  6.0000E-01   1.000E+00   1.000E+00
  7.0000E-01   1.000E+00   1.000E+00
  8.0000E-01   1.000E+00   1.000E+00
  9.0000E-01   1.000E+00   1.000E+00
  1.0000E+00   1.000E+00   1.000E+00

 Time =   0.2400
 Total number of accepted timesteps =   77
 Total number of rejected timesteps =    0

             Total  number (rounded) of     
          Residual  Jacobian    Newton   Lin sys
             evals     evals     iters     iters
 At level 
       1       600        80       200       200

             Maximum  number of   
              Newton iters    Lin sys iters 
 At level 
       1             2             3