Troubleshoot Common ODE Problems

First, check that tspan is not too long. Remember that the solver uses as many time points as necessary to produce a smooth solution. If the ODE function changes on a time scale that is very short compared to tspan, then the solver uses a lot of time steps. Long-time integration is a hard problem. Break tspan into smaller pieces.

If the ODE function does not change noticeably on the tspan interval, it could be that your problem is stiff. Try using one of the stiff solvers ode15s, ode23s, ode23t, or ode23tb.

Finally, make sure that the ODE function is written in an efficient way. The solvers evaluate the derivatives in the ODE function many times. The cost of numerical integration depends critically on the expense of evaluating the ODE function. Rather than recomputing complicated constant parameters at each evaluation, store them in global variables, or calculate them once and pass them to nested functions.