Suggest trying the FortranCalculus compiler, its freeware! Nothing to loose ... FortranCalculus.info/apps/fc-compiler.html . Are you trying to tweak any parameters in order to find the optimum solution? If so, discontinuous functions may slow the solver down, but should still work.

If your problem is a Initial Value Problem (IVP) then no problem at all. A Boundary Value Problem (BVP) may be slow do to the discontinuous functions.

Across the discontinuity you cannot define the derivative so the problem is in the fact you cannot write the ODE not in the numerical methods.

You you are aware of the position of the discontinuity, you can solve the two regions before and after, using some compatibility relation across the discontinuity. Something similar is used for example in the R-H conditions across a normal shock wave.

However, you should detail better your problem.

The rigorous mathematical treatment of ODEs with discontinuous right is feasible but complex, the classical reference are the works by Filippov in the 60s. From the computational viewpoint, a couple of references are

Article A high accuracy method for solving ODEs with discontinuous r...

Article Sliding Motion in Filippov Differential Systems: Theoretical...

thanks @ Luca Bonaventura for your kindly reply.

thanks all of you Phil B Brubaker , Karol Pietrak , Filippo Maria Denaro

Hi Adnan,

I had a similar problem that I solved in Matlab by using the "Events" option in ODE45. You can look into this helpful exemple:

https://fr.mathworks.com/help/matlab/math/ode-event-location.html

Best,

GP

thanks for your reply Giuseppe Pennisi , i have used interpolation in my function. Is that reasonable?

Standard polynomial interpolation performs poorly across discontinuities. Using an 'events' option to include discontinuities is surely preferable.

i see, thanks Luca Bonaventura for your reply.