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Name
Class
Description
Keywords
A1 DETEST
PILA
A very simple linear ODE.
min test set
A2 DETEST
PINLA
A special case of the Riccati equation.
min test set
A3 DETEST
PILA
A simple oscillatory problem; derived from a linear nonautonomous equation with…
nonlinear; simple; periodic
A4 DETEST
PINLA
A logistic curve.

A5 DETEST
PINLA
Derived from a nonautonomous equation with trajectories in the form of a spiral…
homogeneous
ARCH Benchmark 1
PINLB
The LaubLoomis model is a sevendimensional ODE for studying enzymatic activiti…

B1 DETEST
PINLB
The growth of two conflicting populations.
min test set
B2 DETEST
PILB
A linear chemical reaction.
min test set
B3 DETEST
PINLB
A nonlinear chemical reaction.
nonlinear; uncoupled
B4 DETEST
PINLB
The integral surface of a torus.

B5 DETEST
PINLB
Euler equations of motion for a rigid body without external forces.
nonlinear; motion
Bachman's Example
PILB
A linear system with constant coefficients.

C1 DETEST
PILB
A radioactive decay chain with all constants equal to 1. Please note that the su…
decoupled
C2 DETEST
PILB
A radioactive decay chain; Bateman's equation with different decay constants. Pl…
decoupled
C3 DETEST
PILB
Derived from a parabolic partial differential equation; n=10

C4 DETEST
PILC
Derived from a parabolic partial differential equation; n=51.
min test set
C5 DETEST
PINLC
Derived from the five body problem: the motion of 5 outer planets about the sun.
chaotic; min test set
Class D DETEST
PINLB
Orbit equations.

Damped vibrations
PILA


Double Pendulum
PINLB
Equations of motion for the double pendulum model derived automatically with the…
chaotic
E1 DETEST
PILB
Derived from Bessel's equation of order 1/2 with shifted origin (a linear second…
variable coefficients
E2 DETEST
PINLB
Van der Pol oscillator. A nonconservative oscillator with nonlinear damping; s…
chaotic
E3 DETEST
PINLB
Derived from Duffing's equation.

E4 DETEST
PINLB
Derived from the equation of motion for a falling body.

E5 DETEST
PINLB
Derived from a pursuit equation when the path of the pursued is a straight line
nonlinear
Harmonic Oscillator 1
PILA


Harmonic Oscillator 2
PILA
Derived from a second order linear equation with circular solution trajectories.
periodic; min test set
Lambert 1
PILB
Derived from linear equations with variable coefficients.

Lambert 2
PIINLB
Integration must start at t=1 (test intervals: [1,2] for C4/C5; [1,11] for C6).
stiff
Lorenz 1 (Classic Form)
PINLB
A chaotic system of ordinary differential equations. Applications such as simpli…
nonperiodic; chaotic
Lorenz 2 (Jordan NF)
PINLB
See Lorenz 1 (Classic Form); here the Jordan normal form exhibits more chaotic b…
nonperiodic; chaotic; min test set
LotkaVolterra
PIINLB
Predatorprey equations; a system of two firstorder nonlinear differential equ…
periodic; stiff
Nonlinear Degree 3
PINLB

nonlinear
Nonlinear Degree 4
PINLB

nonlinear
Oil reservoir problem
PIINLA
A stiff problem with par0 as the stiffness coefficient (the smaller, the stiffer…
nonperiodic; stiff; min test set
Orbit Equations
PINLB
Shifted orbit equations.

Simple Linear 1
PILA
A simple second order linear equation with constant coefficients.
simple; linear; constant coefficients
Simple Linear 2
PILA
A simple second order equation with constant coefficients.
simple; linear; constant coefficients
Simple Nonlinear 1
PINLA
A nonlinear separable ODE.

Simple Nonlinear 2
PINLA
A nonlinear separable ODE.

Simple Nonlinear 3
PINLA
A nonlinear separable ODE.

Simple Stiff 1
PIILA
A simple linear system of equations which is stiff for certain initial condition…
stiff
Simplified ASM1
PINLC
A simplified biological wastewater treatment process model.

The Roessler Attractor
PINLB
A chaotic system of equations useful for modeling equilibrium in chemical reacti…
chaotic
Two Compartment Model
PILB
A standard example in parameter optimization; describes the way materials or ene…
cooperative; min test set
No matches found.