for 0<t<25 I get beautiful oscillations in columns 3 and 4 of the output file

side remark: You don't need to declare subs k1_1 etc. as variables (e.g. my $k1_1;) (and you could also implement them outside the RK4_... subs, EDIT: did you mean to use them as closures? you don't seem to because you pass them the important params and step is "global" in their scope). EDIT: also you can stop calling subs using the &mysub() notation, instead mysub() is valid.