TEST_ODE
Test Problems for
Initial Value Solvers

TEST_ODE is a FORTRAN90 library which defines a set of test initial value problems for ordinary differential equations.

These problems have the common form:

determine (some values of) the function Y(T)

Y'(T) = F(T,Y)

Y(T₀) = Y₀

A uniform interface makes it easy to solve all the problems automatically, or to concentrate on a single one.

The problems include:

1. Enright and Pryce #A1,
   neqn = 1,
   y' = -y;
2. Enright and Pryce #A2,
   neqn = 1,
   y' = -y^3/2;
3. Enright and Pryce #A3,
   neqn = 1,
   y' = cos(t)*y;
4. Enright and Pryce #A4,
   neqn = 1,
   y' = y*(20-y)/80;
5. Enright and Pryce #A5,
   neqn = 1,
   y' = (y-t)/(y+t);
6. Enright and Pryce #B1,
   neqn = 2,
   y1' = 2*y1*(1-y2)
   y2' = - y2*(1-y1);
7. Enright and Pryce #B2,
   neqn = 3,
   y1' = -y1+y2
   y2' = y1-2*y2+y3
   y3' = y2-y3;
8. Enright and Pryce #B3,
   neqn = 3,
   y1' = -y1
   y2' = y1-y2^2
   y3' = y2^2;
9. Enright and Pryce #B4,
   neqn = 3,
   y1' = (-y2-y1*y3) / sqrt(y1^2+y2^2)
   y2' = (y1-y2*y3) / sqrt(y1^2+y2^2)
   y3' = y1 / sqrt(y1^2+y2^2);
10. Enright and Pryce #B5,
    neqn = 3,
    y1' = y2*y3
    y2' = -y1*y3
    y3' = -0.51*y1*y2;
11. Enright and Pryce #C1,
    neqn = 10;
12. Enright and Pryce #C2,
    neqn = 10;
13. Enright and Pryce #C3,
    neqn = 10;
14. Enright and Pryce #C4,
    neqn = 51;
15. Enright and Pryce #C5,
    neqn = 30;
16. Enright and Pryce #D1,
    neqn = 4;
17. Enright and Pryce #D2,
    neqn = 4;
18. Enright and Pryce #D3,
    neqn = 4;
19. Enright and Pryce #D4,
    neqn = 4;
20. Enright and Pryce #D5,
    neqn = 4;
21. Enright and Pryce #E1,
    neqn = 2;
22. Enright and Pryce #E2,
    neqn = 2;
23. Enright and Pryce #E3,
    neqn = 2;
24. Enright and Pryce #E4,
    neqn = 2;
25. Enright and Pryce #E5,
    neqn = 2;
26. Enright and Pryce #F1,
    neqn = 2;
27. Enright and Pryce #F2,
    neqn = 1;
28. Enright and Pryce #F3,
    neqn = 2;
29. Enright and Pryce #F4,
    neqn = 1;
30. Enright and Pryce #F5,
    neqn = 1;
31. Lotka-Volterra Predator-Prey Equations,
    neqn = 2;
32. The Lorenz System,
    neqn = 3;
33. The Van der Pol equation,
    neqn = 2;
34. The Linearized Damped Pendulum,
    neqn = 2;
35. The Nonlinear Damped Pendulum,
    neqn = 2;
36. Duffing's Equation,
    neqn = 2,
37. Duffing's Equation with Damping and Forcing,
    neqn = 2;
38. Shampine's Ball of Flame,
    neqn = 1,
    y' = y^2-y^3;
39. Polking's First Order System,
    neqn = 1,
    y' = y^2-a*t+b;
40. the Knee problem,
    neqn = 1,
    y' = y*(y-t)/eps;

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TEST_ODE is available in a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

LORENZ_ODE, a FORTRAN90 program which approximates solutions to the Lorenz system, creating output files that can be displayed by Gnuplot.

NMS, a FORTRAN90 library which includes the ddriv package of ODE solvers.

ODE, a FORTRAN90 library which implements the Shampine and Allen ODE solver.

ODEPACK, a FORTRAN77 library which contains nine ODE solvers, including LSODE, LSODES, LSODA, LSODAR, LSODPK, LSODKR, LSODI, LSOIBT, and LSODIS, by Alan Hindmarsh.

RKF45, a FORTRAN90 library which implements a Runge-Kutta-Fehlberg ODE solver.

TOMS648_NSD, a FORTRAN77 library which defines the non-stiff Enright and Pryce test ODE problems, using double precision arithmetic.

References:

1. David Arnold, John Polking,
   Ordinary Differential Equations using Matlab,
   Second Edition,
   Prentice Hall, 1999,
   ISBN: 0130113816.
2. Wayne Enright, John Pryce,
   Two FORTRAN packages for assessing initial value methods,
   ACM Transactions on Mathematical Software,
   Volume 13, Number 1, March 1987, pages 1-27.
3. Wayne Enright, John Pryce,
   Algorithm 648: NSDTST and STDTST,
   ACM Transactions on Mathematical Software,
   Volume 13, Number 1, March 1987, pages 28-34.
4. Thomas Hull, Wayne Enright, BM Fellen, Arthur Sedgwick,
   Comparing numerical methods for ordinary differential equations,
   SIAM Journal on Numerical Analysis,
   Volume 9, 1972, pages 603-637.
5. Cleve Moler,
   Cleve's Corner: Stiff Differential Equations,
   MATLAB News and Notes,
   May 2003, pages 12-13.

1. http://pitagora.dm.uniba.it/~testset/, Test Set for IVP Solvers.
2. http://www.unige.ch/math/~hairer/testset/testset.html Stiff ODE test set of Hairer and Wanner.

Source Code:

• test_ode.f90, the source code;

Examples and Tests:

• test_ode_test.f90, a sample calling program;
• test_ode_test.txt, output from the calling program;

List of Routines:

• CH_CAP capitalizes a single character.
• ERROR_F evaluates the error function ERF(X).
• EULER_TEST uses the Euler method on a test problem.
• P00_AUTONOMOUS reports whether a given problem is autonomous.
• P00_EQUIL returns equilibrium solutions of any problem.
• P00_EULER_STEP takes a single Euler step from (T0,Y0) to (T1,Y1).
• P00_FUN evaluates the derivative function for any problem.
• P00_JAC evaluates the jacobian for any problem.
• P00_NEQN returns the number of equations for any problem.
• P00_RK_STEP takes a single Runge-Kutta step from (T0,Y0) to (T1,Y1).
• P00_SCALE returns scale factors for any problem.
• P00_START returns the starting point for any problem.
• P00_STOP returns the stopping point for any problem.
• P00_TEST_NUM returns the number of problems available.
• P00_TITLE returns the title for any problem.
• P01_AUTONOMOUS reports whether problem p1 is autonomous.
• P01_EQUIL returns equilibrium solutions of problem p1.
• P01_FUN evaluates the function for problem p01.
• P01_JAC evaluates the jacobian for problem p01.
• P01_NEQN returns the number of equations for problem p01.
• P01_SCALE returns scale factors for problem p01.
• P01_START returns the starting point for problem p01.
• P01_STOP returns the stopping point for problem p01.
• P01_TITLE returns the title of problem p01.
• P02_AUTONOMOUS reports whether problem p02 is autonomous.
• P02_EQUIL returns equilibrium solutions of problem p02.
• P02_FUN evaluates the function for problem p02.
• P02_JAC evaluates the jacobian for problem p02.
• P02_NEQN returns the number of equations for problem p02.
• P02_SCALE returns scale factors for problem p02.
• P02_START returns the starting point for problem p02.
• P02_STOP returns the stopping point for problem p02.
• P02_TITLE returns the title of problem p02.
• P03_AUTONOMOUS reports whether problem p03 is autonomous.
• P03_EQUIL returns equilibrium solutions of problem p03.
• P03_FUN evaluates the function for problem p03.
• P03_JAC evaluates the jacobian for problem p03.
• P03_NEQN returns the number of equations for problem p03.
• P03_SCALE returns scale factors for problem p03.
• P03_START returns the starting point for problem p03.
• P03_STOP returns the stopping point for problem p03.
• P03_TITLE returns the title of problem p03.
• P04_AUTONOMOUS reports whether problem p04 is autonomous.
• P04_EQUIL returns equilibrium solutions of problem p04.
• P04_FUN evaluates the function for problem p04.
• P04_JAC evaluates the jacobian for problem p04.
• P04_NEQN returns the number of equations for problem p04.
• P04_SCALE returns scale factors for problem p04.
• P04_START returns the starting point for problem p04.
• P04_STOP returns the stopping point for problem p04.
• P04_TITLE returns the title of problem p04.
• P05_AUTONOMOUS reports whether problem p05 is autonomous.
• P05_EQUIL returns equilibrium solutions of problem p05.
• P05_FUN evaluates the function for problem p05.
• P05_JAC evaluates the jacobian for problem p05.
• P05_NEQN returns the number of equations for problem p05.
• P05_SCALE returns scale factors for problem p05.
• P05_START returns the starting point for problem p05.
• P05_STOP returns the stopping point for problem p05.
• P05_TITLE returns the title of problem p05.
• P06_AUTONOMOUS reports whether problem p06 is autonomous.
• P06_EQUIL returns equilibrium solutions of problem p06.
• P06_FUN evaluates the function for problem p06.
• P06_JAC evaluates the jacobian for problem p06.
• P06_NEQN returns the number of equations for problem p06.
• P06_SCALE returns scale factors for problem p06.
• P06_START returns the starting point for problem p06.
• P06_STOP returns the stopping point for problem p06.
• P06_TITLE returns the title of problem p06.
• P07_AUTONOMOUS reports whether problem p07 is autonomous.
• P07_EQUIL returns equilibrium solutions of problem p07.
• P07_FUN evaluates the function for problem p07.
• P07_JAC evaluates the jacobian for problem p07.
• P07_NEQN returns the number of equations for problem p07.
• P07_SCALE returns scale factors for problem p07.
• P07_START returns the starting point for problem p07.
• P07_STOP returns the stopping point for problem p07.
• P07_TITLE returns the title of problem p07.
• P08_AUTONOMOUS reports whether problem p08 is autonomous.
• P08_EQUIL returns equilibrium solutions of problem p08.
• P08_FUN evaluates the function for problem p08.
• P08_JAC evaluates the jacobian for problem p08.
• P08_NEQN returns the number of equations for problem p08.
• P08_SCALE returns scale factors for problem p08.
• P08_START returns the starting point for problem p08.
• P08_STOP returns the stopping point for problem p08.
• P08_TITLE returns the title of problem p08.
• P09_AUTONOMOUS reports whether problem p09 is autonomous.
• P09_EQUIL returns equilibrium solutions of problem p09.
• P09_FUN evaluates the function for problem p09.
• P09_JAC evaluates the jacobian for problem p09.
• P09_NEQN returns the number of equations for problem p09.
• P09_SCALE returns scale factors for problem p09.
• P09_START returns the starting point for problem p09.
• P09_STOP returns the stopping point for problem p09.
• P09_TITLE returns the title of problem p09.
• P10_AUTONOMOUS reports whether problem p10 is autonomous.
• P10_EQUIL returns equilibrium solutions of problem p10.
• P10_FUN evaluates the function for problem p10.
• P10_JAC evaluates the jacobian for problem p10.
• P10_NEQN returns the number of equations for problem p10.
• P10_SCALE returns scale factors for problem p10.
• P10_START returns the starting point for problem p10.
• P10_STOP returns the stopping point for problem p10.
• P10_TITLE returns the title of problem p10.
• P11_AUTONOMOUS reports whether problem p11 is autonomous.
• P11_EQUIL returns equilibrium solutions of problem p11.
• P11_FUN evaluates the function for problem p11.
• P11_JAC evaluates the jacobian for problem p11.
• P11_NEQN returns the number of equations for problem p11.
• P11_SCALE returns scale factors for problem p11.
• P11_START returns the starting point for problem p11.
• P11_STOP returns the stopping point for problem p11.
• P11_TITLE returns the title of problem p11.
• P12_AUTONOMOUS reports whether problem p12 is autonomous.
• P12_EQUIL returns equilibrium solutions of problem p12.
• P12_FUN evaluates the function for problem p12.
• P12_JAC evaluates the jacobian for problem p12.
• P12_NEQN returns the number of equations for problem p12.
• P12_SCALE returns scale factors for problem p12.
• P12_START returns the starting point for problem p12.
• P12_STOP returns the stopping point for problem p12.
• P12_TITLE returns the title of problem p12.
• P13_AUTONOMOUS reports whether problem p13 is autonomous.
• P13_EQUIL returns equilibrium solutions of problem p13.
• P13_FUN evaluates the function for problem p13.
• P13_JAC evaluates the jacobian for problem p13.
• P13_NEQN returns the number of equations for problem p13.
• P13_SCALE returns scale factors for problem p13.
• P13_START returns the starting point for problem p13.
• P13_STOP returns the stopping point for problem p13.
• P13_TITLE returns the title of problem p13.
• P14_AUTONOMOUS reports whether problem p14 is autonomous.
• P14_EQUIL returns equilibrium solutions of problem p14.
• P14_FUN evaluates the function for problem p14.
• P14_JAC evaluates the jacobian for problem p14.
• P14_NEQN returns the number of equations for problem p14.
• P14_SCALE returns scale factors for problem p14.
• P14_START returns the starting point for problem p14.
• P14_STOP returns the stopping point for problem p14.
• P14_TITLE returns the title of problem p14.
• P15_AUTONOMOUS reports whether problem p15 is autonomous.
• P15_EQUIL returns equilibrium solutions of problem p15.
• P15_FUN evaluates the function for problem p15.
• P15_JAC evaluates the jacobian for problem p15.
• P15_NEQN returns the number of equations for problem p15.
• P15_PARAM handles the parameters for problem p15.
• P15_SCALE returns scale factors for problem p15.
• P15_START returns the starting point for problem p15.
• P15_STOP returns the stopping point for problem p15.
• P15_TITLE returns the title of problem p15.
• P16_AUTONOMOUS reports whether problem p16 is autonomous.
• P16_EQUIL returns equilibrium solutions of problem p16.
• P16_FUN evaluates the function for problem p16.
• P16_JAC evaluates the jacobian for problem p16.
• P16_NEQN returns the number of equations for problem p16.
• P16_PARAM handles the parameters for problem p16.
• P16_SCALE returns scale factors for problem p16.
• P16_START returns the starting point for problem p16.
• P16_STOP returns the stopping point for problem p16.
• P16_TITLE returns the title of problem p16.
• P17_AUTONOMOUS reports whether problem p17 is autonomous.
• P17_EQUIL returns equilibrium solutions of problem p17.
• P17_FUN evaluates the function for problem p17.
• P17_JAC evaluates the jacobian for problem p17.
• P17_NEQN returns the number of equations for problem p17.
• P17_PARAM handles the parameters for problem p17.
• P17_SCALE returns scale factors for problem p17.
• P17_START returns the starting point for problem p17.
• P17_STOP returns the stopping point for problem p17.
• P17_TITLE returns the title of problem p17.
• P18_AUTONOMOUS reports whether problem p18 is autonomous.
• P18_EQUIL returns equilibrium solutions of problem p18.
• P18_FUN evaluates the function for problem p18.
• P18_JAC evaluates the jacobian for problem p18.
• P18_NEQN returns the number of equations for problem p18.
• P18_PARAM handles the parameters for problem p18.
• P18_SCALE returns scale factors for problem p18.
• P18_START returns the starting point for problem p18.
• P18_STOP returns the stopping point for problem p18.
• P18_TITLE returns the title of problem p18.
• P19_AUTONOMOUS reports whether problem p19 is autonomous.
• P19_EQUIL returns equilibrium solutions of problem p19.
• P19_FUN evaluates the function for problem p19.
• P19_JAC evaluates the jacobian for problem p19.
• P19_NEQN returns the number of equations for problem p19.
• P19_PARAM handles the parameters for problem p19.
• P19_SCALE returns scale factors for problem p19.
• P19_START returns the starting point for problem p19.
• P19_STOP returns the stopping point for problem p19.
• P19_TITLE returns the title of problem p19.
• P20_AUTONOMOUS reports whether problem p20 is autonomous.
• P20_EQUIL returns equilibrium solutions of problem p20.
• P20_FUN evaluates the function for problem p20.
• P20_JAC evaluates the jacobian for problem p20.
• P20_NEQN returns the number of equations for problem p20.
• P20_PARAM handles the parameters for problem p20.
• P20_SCALE returns scale factors for problem p20.
• P20_START returns the starting point for problem p20.
• P20_STOP returns the stopping point for problem p20.
• P20_TITLE returns the title of problem p20.
• P21_AUTONOMOUS reports whether problem p21 is autonomous.
• P21_EQUIL returns equilibrium solutions of problem p21.
• P21_FUN evaluates the function for problem p21.
• P21_JAC evaluates the jacobian for problem p21.
• P21_NEQN returns the number of equations for problem p21.
• P21_SCALE returns scale factors for problem p21.
• P21_START returns the starting point for problem p21.
• P21_STOP returns the stopping point for problem p21.
• P21_TITLE returns the title of problem p21.
• P22_AUTONOMOUS reports whether problem p22 is autonomous.
• P22_EQUIL returns equilibrium solutions of problem p22.
• P22_FUN evaluates the function for problem p22.
• P22_JAC evaluates the jacobian for problem p22.
• P22_NEQN returns the number of equations for problem p22.
• P22_SCALE returns scale factors for problem p22.
• P22_START returns the starting point for problem p22.
• P22_STOP returns the stopping point for problem p22.
• P22_TITLE returns the title of problem p22.
• P23_AUTONOMOUS reports whether problem p23 is autonomous.
• P23_EQUIL returns equilibrium solutions of problem p23.
• P23_FUN evaluates the function for problem p23.
• P23_JAC evaluates the jacobian for problem p23.
• P23_NEQN returns the number of equations for problem p23.
• P23_SCALE returns scale factors for problem p23.
• P23_START returns the starting point for problem p23.
• P23_STOP returns the stopping point for problem p23.
• P23_TITLE returns the title of problem p23.
• P24_AUTONOMOUS reports whether problem p24 is autonomous.
• P24_EQUIL returns equilibrium solutions of problem p24.
• P24_FUN evaluates the function for problem p24.
• P24_JAC evaluates the jacobian for problem p24.
• P24_NEQN returns the number of equations for problem p24.
• P24_SCALE returns scale factors for problem p24.
• P24_START returns the starting point for problem p24.
• P24_STOP returns the stopping point for problem p24.
• P24_TITLE returns the title of problem p24.
• P25_AUTONOMOUS reports whether problem p25 is autonomous.
• P25_EQUIL returns equilibrium solutions of problem p25.
• P25_FUN evaluates the function for problem p25.
• P25_JAC evaluates the jacobian for problem p25.
• P25_NEQN returns the number of equations for problem p25.
• P25_SCALE returns scale factors for problem p25.
• P25_START returns the starting point for problem p25.
• P25_STOP returns the stopping point for problem p25.
• P25_TITLE returns the title of problem p25.
• P26_AUTONOMOUS reports whether problem p26 is autonomous.
• P26_EQUIL returns equilibrium solutions of problem p26.
• P26_FUN evaluates the function for problem p26.
• P26_JAC evaluates the jacobian for problem p26.
• P26_NEQN returns the number of equations for problem p26.
• P26_PARAM handles the parameters for problem p26.
• P26_SCALE returns scale factors for problem p26.
• P26_START returns the starting point for problem p26.
• P26_STOP returns the stopping point for problem p26.
• P26_TITLE returns the title of problem p26.
• P27_AUTONOMOUS reports whether problem p27 is autonomous.
• P27_EQUIL returns equilibrium solutions of problem p27.
• P27_FUN evaluates the function for problem p27.
• P27_JAC evaluates the jacobian for problem p27.
• P27_NEQN returns the number of equations for problem p27.
• P27_SCALE returns scale factors for problem p27.
• P27_START returns the starting point for problem p27.
• P27_STOP returns the stopping point for problem p27.
• P27_TITLE returns the title of problem p27.
• P28_AUTONOMOUS reports whether problem p14 is autonomous.
• P28_EQUIL returns equilibrium solutions of problem p28.
• P28_FUN evaluates the function for problem p28.
• P28_JAC evaluates the jacobian for problem p28.
• P28_NEQN returns the number of equations for problem p28.
• P28_SCALE returns scale factors for problem p28.
• P28_START returns the starting point for problem p28.
• P28_STOP returns the stopping point for problem p28.
• P28_TITLE returns the title of problem p28.
• P29_AUTONOMOUS reports whether problem p29 is autonomous.
• P29_EQUIL returns equilibrium solutions of problem p29.
• P29_FUN evaluates the function for problem p29.
• P29_JAC evaluates the jacobian for problem p29.
• P29_NEQN returns the number of equations for problem p29.
• P29_SCALE returns scale factors for problem p29.
• P29_START returns the starting point for problem p29.
• P29_STOP returns the stopping point for problem p29.
• P29_TITLE returns the title of problem p29.
• P30_AUTONOMOUS reports whether problem p30 is autonomous.
• P30_EQUIL returns equilibrium solutions of problem p30.
• P30_FUN evaluates the function for problem p30.
• P30_JAC evaluates the jacobian for problem p30.
• P30_NEQN returns the number of equations for problem p30.
• P30_SCALE returns scale factors for problem p30.
• P30_START returns the starting point for problem p30.
• P30_STOP returns the stopping point for problem p30.
• P30_TITLE returns the title of problem p30.
• P31_AUTONOMOUS reports whether problem p31 is autonomous.
• P31_EQUIL returns equilibrium solutions of problem p31.
• P31_FUN evaluates the function for problem p31.
• P31_JAC evaluates the jacobian for problem p31.
• P31_NEQN returns the number of equations for problem p31.
• P31_PARAM handles the parameters for problem p31.
• P31_SCALE returns scale factors for problem p31.
• P31_START returns the starting point for problem p31.
• P31_STOP returns the stopping point for problem p31.
• P31_TITLE returns the title of problem p31.
• P32_AUTONOMOUS reports whether problem p32 is autonomous.
• P32_EQUIL returns equilibrium solutions of problem p32.
• P32_FUN evaluates the function for problem p32.
• P32_JAC evaluates the jacobian for problem p32.
• P32_NEQN returns the number of equations for problem p32.
• P32_PARAM handles the parameters for problem p32.
• P32_SCALE returns scale factors for problem p32.
• P32_START returns the starting point for problem p32.
• P32_STOP returns the stopping point for problem p32.
• P32_TITLE returns the title of problem p32.
• P33_AUTONOMOUS reports whether problem p33 is autonomous.
• P33_EQUIL returns equilibrium solutions of problem p33.
• P33_FUN evaluates the function for problem p33.
• P33_JAC evaluates the jacobian for problem p33.
• P33_NEQN returns the number of equations for problem p33.
• P33_PARAM handles the parameters for problem p33.
• P33_SCALE returns scale factors for problem p33.
• P33_START returns the starting point for problem p33.
• P33_STOP returns the stopping point for problem p33.
• P33_TITLE returns the title of problem p33.
• P34_AUTONOMOUS reports whether problem p34 is autonomous.
• P34_EQUIL returns equilibrium solutions of problem p34.
• P34_FUN evaluates the function for problem p34.
• P34_JAC evaluates the jacobian for problem p34.
• P34_NEQN returns the number of equations for problem p34.
• P34_PARAM handles the parameters for problem p34.
• P34_SCALE returns scale factors for problem p34.
• P34_START returns the starting point for problem p34.
• P34_STOP returns the stopping point for problem p34.
• P34_TITLE returns the title of problem p34.
• P35_AUTONOMOUS reports whether problem p35 is autonomous.
• P35_EQUIL returns equilibrium solutions of problem p35.
• P35_FUN evaluates the function for problem p35.
• P35_JAC evaluates the jacobian for problem p35.
• P35_NEQN returns the number of equations for problem p35.
• P35_PARAM handles the parameters for problem p35.
• P35_SCALE returns scale factors for problem p35.
• P35_START returns the starting point for problem p35.
• P35_STOP returns the stopping point for problem p35.
• P35_TITLE returns the title of problem p35.
• P36_AUTONOMOUS reports whether problem p36 is autonomous.
• P36_EQUIL returns equilibrium solutions of problem p36.
• P36_FUN evaluates the function for problem p36.
• P36_JAC evaluates the jacobian for problem p36.
• P36_NEQN returns the number of equations for problem p36.
• P36_SCALE returns scale factors for problem p36.
• P36_START returns the starting point for problem p36.
• P36_STOP returns the stopping point for problem p36.
• P36_TITLE returns the title of problem p36.
• P37_AUTONOMOUS reports whether problem p37 is autonomous.
• P37_EQUIL returns equilibrium solutions of problem p37.
• P37_FUN evaluates the function for problem p37.
• P37_JAC evaluates the jacobian for problem p37.
• P37_NEQN returns the number of equations for problem p37.
• P37_PARAM handles the parameters for problem p37.
• P37_SCALE returns scale factors for problem p37.
• P37_START returns the starting point for problem p37.
• P37_STOP returns the stopping point for problem p37.
• P37_TITLE returns the title of problem p37.
• P38_AUTONOMOUS reports whether problem p38 is autonomous.
• P38_EQUIL returns equilibrium solutions of problem p38.
• P38_FUN evaluates the function for problem p38.
• P38_JAC evaluates the jacobian for problem p38.
• P38_NEQN returns the number of equations for problem p38.
• P38_PARAM handles the parameters for problem p38.
• P38_SCALE returns scale factors for problem p38.
• P38_START returns the starting point for problem p38.
• P38_STOP returns the stopping point for problem p38.
• P38_TITLE returns the title of problem p38.
• P39_AUTONOMOUS reports whether problem p39 is autonomous.
• P39_EQUIL returns equilibrium solutions of problem p39.
• P39_FUN evaluates the function for problem p39.
• P39_JAC evaluates the jacobian for problem p39.
• P39_NEQN returns the number of equations for problem p39.
• P39_PARAM handles the parameters for problem p39.
• P39_SCALE returns scale factors for problem p39.
• P39_START returns the starting point for problem p39.
• P39_STOP returns the stopping point for problem p39.
• P39_TITLE returns the title of problem p39.
• P40_AUTONOMOUS reports whether problem p40 is autonomous.
• P40_EQUIL returns equilibrium solutions of problem p40.
• P40_FUN evaluates the function for problem p40.
• P40_JAC evaluates the jacobian for problem p40.
• P40_NEQN returns the number of equations for problem p40.
• P40_PARAM handles the parameters for problem p40.
• P40_SCALE returns scale factors for problem p40.
• P40_START returns the starting point for problem p40.
• P40_STOP returns the stopping point for problem p40.
• P40_TITLE returns the title of problem p40.
• R8_CUBE_ROOT returns the cube root of a real number.
• R8_SIGN returns the sign of an R8.
• R8_UNIFORM_AB returns a scaled pseudorandom R8.
• R8MAT_NORM_FRO_AFFINE returns the Frobenius norm of an R8MAT difference.
• R8VEC_UNIFORM_ABVEC returns a scaled pseudorandom R8VEC.
• RK_TEST uses a Runge-Kutta method on a test problem.
• S_EQI is a case insensitive comparison of two strings for equality.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.