ode solvers state solution numerical errors

Dear All,

I am wondering about the numerical errors in the state solution obtained from using the ode solvers in MATLAB. How accurate are the state solutions obtained from the solvers? Could you please explain in terms of the discretization error, round off error, and floating point arithematics, in terms of how much error is expected using the big O notation?

Thank you for your help!

Sincerely,

Tae

Answer 1

[Torsten]

Look at the references at the bottom of the pages describing the codes, e.g. at the bottom of

https://de.mathworks.com/help/matlab/ref/ode15s.html

and

https://de.mathworks.com/help/matlab/ref/ode45.html

[Taehun Kim]

Thank you! I looked at the reference but they are quite hard for me to fully understand. I am looking for the possible error in the numerical solution of the ODEs solved by MATLAB ode solvers. In a model that I have, there is a term constructed with component-wise subtracting two vectors, each defined by multiplying states variables, that are in the similar magnitude, hance causing the catastrpohic cancellation problem. The order of the magnitude in the comptued difference term is and we multiply the vector by a large constant to obtain the final result. I am wondering if the state solution error is behind the scene, causing the erratic behavior in my solution.

[Taehun Kim]

Thank you for your help! I talked to my friends and we learned that we can adjust the absolute and relative tolerances to get rid of the errorenous behavior!