```
nag_ode_ivp_bdf_zero_simple (d02ejc) Example Program Results

Case 1: calculating Jacobian internally
intermediate output, root-finding

Calculation with tol =    1.0e-03
X         Y(1)         Y(2)         Y(3)
0.00       1.0000      0.00000       0.0000
(User-supplied callback g, first invocation.)
(User-supplied callback fcn, first invocation.)
2.00       0.9416      0.00003       0.0583
4.00       0.9055      0.00002       0.0945
Root of Y(1)-0.9 at 4.377
Solution is  0.9000  0.00002  0.1000

Calculation with tol =    1.0e-04
X         Y(1)         Y(2)         Y(3)
0.00       1.0000      0.00000       0.0000
2.00       0.9416      0.00003       0.0584
4.00       0.9055      0.00002       0.0945
Root of Y(1)-0.9 at 4.377
Solution is  0.9000  0.00002  0.1000

Case 2: calculating Jacobian by pederv
intermediate output, root-finding

Calculation with tol =    1.0e-03
X         Y(1)         Y(2)         Y(3)
(User-supplied callback pederv, first invocation.)
0.00       1.0000      0.00000       0.0000
2.00       0.9416      0.00003       0.0583
4.00       0.9055      0.00002       0.0945
Root of Y(1)-0.9 at 4.377
Solution is  0.9000  0.00002  0.1000

Calculation with tol =    1.0e-04
X         Y(1)         Y(2)         Y(3)
0.00       1.0000      0.00000       0.0000
2.00       0.9416      0.00003       0.0584
4.00       0.9055      0.00002       0.0945
Root of Y(1)-0.9 at 4.377
Solution is  0.9000  0.00002  0.1000

Case 3: calculating Jacobian internally
no intermediate output, root-finding

Calculation with tol =    1.0e-03
Root of Y(1)-0.9 at 4.377
Solution is  0.9000  0.00002  0.1000

Calculation with tol =    1.0e-04
Root of Y(1)-0.9 at 4.377
Solution is  0.9000  0.00002  0.1000

Case 4: calculating Jacobian internally
intermediate output, no root-finding

Calculation with tol =    1.0e-03
X         Y(1)         Y(2)         Y(3)
0.00       1.0000      0.00000       0.0000
2.00       0.9416      0.00003       0.0583
4.00       0.9055      0.00002       0.0945
6.00       0.8793      0.00002       0.1207
8.00       0.8586      0.00002       0.1414
10.00       0.8414      0.00002       0.1586
10.00       0.8414      0.00002       0.1586

Calculation with tol =    1.0e-04
X         Y(1)         Y(2)         Y(3)
0.00       1.0000      0.00000       0.0000
2.00       0.9416      0.00003       0.0584
4.00       0.9055      0.00002       0.0945
6.00       0.8793      0.00002       0.1207
8.00       0.8585      0.00002       0.1414
10.00       0.8414      0.00002       0.1586
10.00       0.8414      0.00002       0.1586

Case 5: calculating Jacobian internally
no intermediate output, no root-finding (integrate to xend)

Calculation with tol =    1.0e-03
X         Y(1)         Y(2)         Y(3)
0.00       1.0000      0.00000       0.0000
10.00       0.8414      0.00002       0.1586

Calculation with tol =    1.0e-04
X         Y(1)         Y(2)         Y(3)
0.00       1.0000      0.00000       0.0000
10.00       0.8414      0.00002       0.1586
```