How do i solve huge coupled first order differential equations

Hello all,

I have a system of 25 coupled first order constant coefficient linear differential equations (time evolution of a multistep reaction). The problem is I want to calculate the solution upto say 100 microseconds. I am able to calculate upto 1 microsecond using ode45 (which itself gives an array of 16912805 data points). Anything 3 microseconds and above crashes my computer completely.

Is there any way I can solve this problem? a user defined function or an ode solver which allows me to input the timestep (because when i read the documentation for ode45, i found out that the time step is controlled internally and thus i cant specify a larger timestep to save computation time).

[Torsten]

Don't use ode45 for chemical reaction problems, but ode15s instead.

[Arun S]

Thank you ode15s drastically reduced my computation time.

Answer 1

[Star Strider]

The integration times are adaptive, however it is possible control the points at which the differential equation system is evaluated and appear in the output.

For example to integrate at 100 points between 0 and 100 microseconds, this could work:

tspan = linspace(0, 1E-4, 100);

Use that (or something similar) for ‘tspan’ in your system to see if it does what you want.

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[Arun S]

Thank you so much. This along with using ode15s solved my problem.

[Star Strider]

As always, my pleasure!

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