ODE Solvers

A lab done as part of a course in numeric methods. Contains naive implementations of the following ODE solvers:

• Explicit Euler's method

• Implicit Euler's method

• Symmetric Euler's method

• 2nd order Runge-Kutta method

• 4th order Runge-Kutta method

• 4th order Runge-Kutta method (with adaptive step size)

• 4th order predictor-corrector method

• 4th order Adams method (linear multistep method)

Compilation

• Requires C++17 support

Dependencies

• Eigen 3.4.0.

Usage

Use "odeproblems.hpp" to config equation, initial conditions, precision and etc.

All solutions are saved to "[output]/" by default, where they can be visualzed by launching "Visualization.nb" (requires a valid WolframMathematica license).

Visualization examples

Harmonic equation solution can be used to show how some methods affect total energy of a system. Here, implicit Euler's method shows its tendency to loose energy over time, while symmetric Euler is conservative:

By solving a problem for a small time interval on a given grid one can obtain phase portrait of a system:

Since there is no inherent limitation of system dimensionality, the same can be done in 3D:

Version History

• 00.01

  ** Final release

License

This project is licensed under the MIT License - see the LICENSE.md file for details