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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 non-autonomous equation with…
non-linear; simple; periodic
A4 DETEST
PINLA
A logistic curve.
-
A5 DETEST
PINLA
Derived from a non-autonomous equation with trajectories in the form of a spiral…
homogeneous
ARCH Benchmark 1
PINLB
The Laub-Loomis model is a seven-dimensional 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.
non-linear; uncoupled
B4 DETEST
PINLB
The integral surface of a torus.
-
B5 DETEST
PINLB
Euler equations of motion for a rigid body without external forces.
non-linear; 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 non-conservative oscillator with non-linear 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
non-linear
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…
non-periodic; chaotic
Lorenz 2 (Jordan NF)
PINLB
See Lorenz 1 (Classic Form); here the Jordan normal form exhibits more chaotic b…
non-periodic; chaotic; min test set
Lotka-Volterra
PIINLB
Predator-prey equations; a system of two first-order non-linear differential equ…
periodic; stiff
Nonlinear Degree 3
PINLB
-
non-linear
Nonlinear Degree 4
PINLB
-
non-linear
Oil reservoir problem
PIINLA
A stiff problem with par0 as the stiffness coefficient (the smaller, the stiffer…
non-periodic; 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 non-linear separable ODE.
-
Simple Nonlinear 2
PINLA
A non-linear separable ODE.
-
Simple Nonlinear 3
PINLA
A non-linear 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.