lindberg_ode

lindberg_ode, a Python code which sets up and solves a system of 4 ordinary differential equations (ODE) which are very stiff.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

lindberg_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

lindberg_exact, a Python code which evaluates the exact solution of the Lindberg ordinary differential equations (ODE), a system that is extremely difficult to solve accurately.

python_ode, a Python code which sets up various systems of ordinary differential equations (ODE).

References:

1. William Layton, Wenlong Pei, Catalin Trenchea,
   Time step adaptivity in the method of Dahlquist, Liniger, and Nevanlinna,
   Advances in Computational Science and Engineering,
   Volume 1, Number 3, September 2023, pages 320-350.
2. Bengt Lindberg,
   On a dangerous property of methods for stiff differential equations,
   BIT Numerical Mathematics,
   Volume 14, 1974, pages 430-436.
3. Daniel Watanabe, Qasim Sheikh,
   One-leg formulas for stiff ordinary differential equations,
   SIAM Journal on Scientific and Statistical Computing,
   Volume 5, Number 2, June 1984, pages 489-496.

Source Code:

• lindberg_ode.py, the source code.
• lindberg_ode.sh, runs all the tests.
• lindberg_ode.txt, the output file.

• lindberg_solve_ivp_y1.png, a plot of y1(t).
• lindberg_solve_ivp_y2.png, a plot of y2(t).
• lindberg_solve_ivp_y3.png, a plot of y3(t).
• lindberg_solve_ivp_y4.png, a plot of y4(t).