ODE Test Problems

ODE Test Problems (OTP) is an object-oriented MATLAB/GNU Octave package offering a broad range of ordinary differential equations, partial differential equations, and differential algebraic equations which can be used to test numerical methods such as time-steppers and data assimilation methods. It contains problems that are linear and nonlinear, autonomous and nonautonomous, scalar and high-dimensional, and stiff and nonstiff. OTP also supports partitioned systems for testing IMEX methods, multirate methods, and other partitioned schemes. Many problems come from real-world applications in fields such as chemistry, astrophysics, meteorology, and electrical engineering. OTP's interface provides a simple and standardized way to access problem parameters, the right-hand side function, the Jacobian matrix, and other properties. Each problem is equipped with functions for computing the solution, plotting the solution, and creating a movie.

Although OTP is currently under development, the public API is quite stable. We are currently writing full documentation in order to release version 1.0.0.

If there is a test problem, additional RHS property, or new functionality you would like added to OTP, we encourage you to let us know via a GitHub issue. We also accept pull requests that adhere to our contributing guide.

Installation

OTP can be installed as a local MATLAB toolbox or Octave package by running

OTP.install

from the root directory of the project. If no longer needed, it can be uninstalled with OTP.uninstall.

Example

% Create a problem
problem = otp.lotkavolterra.presets.Canonical;

% Solve the problem
sol = problem.solve('RelTol', 1e-10);

% Plot the solution
problem.plot(sol);

% Adjust a parameter
problem.Parameters.PreyDeathRate = 2;

% Manually use a MATLAB ODE solver to solve the problem
options = odeset('Jacobian', problem.RHS.Jacobian);
[t, y] = ode15s(problem.RHS.F, problem.TimeSpan, problem.Y0, options);

% Plot the phase space with a custom title
problem.plotPhaseSpace(t, y, 'Title', 'The Circle of Life');

% Create a movie and write to file
mov = problem.movie(t, y, 'Save', 'lotka-volterra.avi');