reaction_twoway_ode

reaction_twoway_ode, a Python code which sets up and solves the ordinary differential equations (ODE) which model a two-way chemical reaction between species W1 and W2.

The reference suggests an experiment in which the Forward Euler method is used, with a timestep of 1/50. The problem is to be solved three times, with the second reaction coefficient, k2, set to 10 (the default), 100, and 1000. The value k2=1000 makes the solution very difficult to compute accurately.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

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

Related Data and codes:

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

References:

1. Willem Hundsdorfer, Jan Verwer,
   Numerical solution of time-dependent advection-diffusion-reaction equations,
   Springer, 2003
   ISBN: 978-3-662-09017-6

Source Code:

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

• reaction_twoway_euler_conservation.png, displays the conserved quantity.
• reaction_twoway_euler_solution.png, displays the solution.

• reaction_twoway_midpoint_conservation.png, displays the conserved quantity.
• reaction_twoway_midpoint_solution.png, displays the solution.

• reaction_twoway_solve_ivp_conservation.png, displays the conserved quantity.
• reaction_twoway_solve_ivp_solution.png, displays the solution.