test_ode
test_ode,
a FORTRAN90 code which
defines a set of test initial
value problems for ordinary differential equations (ODE).
These problems have the common form:
determine (some values of) the function Y(T)
given
Y'(T) = F(T,Y)
with initial value
Y(T_{0}) = Y_{0}
A uniform interface makes it easy to solve all the problems
automatically, or to concentrate on a single one.
The problems include:

Enright and Pryce #A1,
neqn = 1,
y' = y;

Enright and Pryce #A2,
neqn = 1,
y' = y^3/2;

Enright and Pryce #A3,
neqn = 1,
y' = cos(t)*y;

Enright and Pryce #A4,
neqn = 1,
y' = y*(20y)/80;

Enright and Pryce #A5,
neqn = 1,
y' = (yt)/(y+t);

Enright and Pryce #B1,
neqn = 2,
y1' = 2*y1*(1y2)
y2' =  y2*(1y1);

Enright and Pryce #B2,
neqn = 3,
y1' = y1+y2
y2' = y12*y2+y3
y3' = y2y3;

Enright and Pryce #B3,
neqn = 3,
y1' = y1
y2' = y1y2^2
y3' = y2^2;

Enright and Pryce #B4,
neqn = 3,
y1' = (y2y1*y3) / sqrt(y1^2+y2^2)
y2' = (y1y2*y3) / sqrt(y1^2+y2^2)
y3' = y1 / sqrt(y1^2+y2^2);

Enright and Pryce #B5,
neqn = 3,
y1' = y2*y3
y2' = y1*y3
y3' = 0.51*y1*y2;

Enright and Pryce #C1,
neqn = 10;

Enright and Pryce #C2,
neqn = 10;

Enright and Pryce #C3,
neqn = 10;

Enright and Pryce #C4,
neqn = 51;

Enright and Pryce #C5,
neqn = 30;

Enright and Pryce #D1,
neqn = 4;

Enright and Pryce #D2,
neqn = 4;

Enright and Pryce #D3,
neqn = 4;

Enright and Pryce #D4,
neqn = 4;

Enright and Pryce #D5,
neqn = 4;

Enright and Pryce #E1,
neqn = 2;

Enright and Pryce #E2,
neqn = 2;

Enright and Pryce #E3,
neqn = 2;

Enright and Pryce #E4,
neqn = 2;

Enright and Pryce #E5,
neqn = 2;

Enright and Pryce #F1,
neqn = 2;

Enright and Pryce #F2,
neqn = 1;

Enright and Pryce #F3,
neqn = 2;

Enright and Pryce #F4,
neqn = 1;

Enright and Pryce #F5,
neqn = 1;

LotkaVolterra PredatorPrey Equations,
neqn = 2;

The Lorenz System,
neqn = 3;

The Van der Pol equation,
neqn = 2;

The Linearized Damped Pendulum,
neqn = 2;

The Nonlinear Damped Pendulum,
neqn = 2;

Duffing's Equation,
neqn = 2,

Duffing's Equation with Damping and Forcing,
neqn = 2;

Shampine's Ball of Flame,
neqn = 1,
y' = y^2y^3;

Polking's First Order System,
neqn = 1,
y' = y^2a*t+b;

the Knee problem,
neqn = 1,
y' = y*(yt)/eps;
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the MIT license
Languages:
test_ode is available in
a FORTRAN90 version and
a MATLAB version.
Related Data and Programs:
test_ode_test
lorenz_ode,
a FORTRAN90 code which
approximates solutions to the Lorenz system,
creating output files that can be displayed by Gnuplot.
midpoint,
a FORTRAN90 code which
solves one or more ordinary differential equations (ODEs)
using the midpoint method.
nms,
a FORTRAN90 code which
includes the ddriv() package of ODE solvers.
ODE,
a FORTRAN90 code which
implements the Shampine and Allen ODE solver.
predator_prey_ode,
a FORTRAN90 code which
solves a pair of predator prey ordinary differential equations (ODE's).
RKF45,
a FORTRAN90 code which
implements a RungeKuttaFehlberg ODE solver.
spring,
a FORTRAN90 code which
shows how gnuplot graphics can be used to illustrate
a solution of the ordinary differential equation (ODE) that describes
the motion of a weight attached to a spring.
stiff_ode,
a FORTRAN90 code which
considers an ordinary differential equation (ODE) which is
an example of a stiff ODE.
References:

David Arnold, John Polking,
Ordinary Differential Equations using Matlab,
Second Edition,
Prentice Hall, 1999,
ISBN: 0130113816.

Wayne Enright, John Pryce,
Two FORTRAN packages for assessing initial value methods,
ACM Transactions on Mathematical Software,
Volume 13, Number 1, March 1987, pages 127.

Wayne Enright, John Pryce,
Algorithm 648:
NSDTST and STDTST,
ACM Transactions on Mathematical Software,
Volume 13, Number 1, March 1987, pages 2834.

Thomas Hull, Wayne Enright, BM Fellen, Arthur Sedgwick,
Comparing numerical methods for ordinary differential equations,
SIAM Journal on Numerical Analysis,
Volume 9, 1972, pages 603637.

Cleve Moler,
Cleve's Corner: Stiff Differential Equations,
MATLAB News and Notes,
May 2003, pages 1213.

http://pitagora.dm.uniba.it/~testset/,
Test Set for IVP Solvers.

http://www.unige.ch/math/~hairer/testset/testset.html
Stiff ODE test set of Hairer and Wanner.
Source Code:
Last revised on 02 October 2023.