Which method of wich order should I choose for a non-smooth ODE $~x'=f(x,t)~$ with $~f~$ only two times derivable with continuity?
Should I choose a method of order two? or a method of order four as the Runge Kutta $4$ still gives convenient results?
From what I understood a method of order $4$ would work correctly only for $~f~$ sufficient smooth (not my case)...is that right?
Thanks to everybody!
On a theoretical basis, high-order methods are obtained by matching the coefficients of the derivatives in the Taylor expansions of the exact and numerical solutions. Hence, yes, you would need high regularity to obtain high order. In my experience though, you can get in practice higher order of convergence for non-smooth functions (which should not be the case).