I definitely understand nothing about what this all is supposed to do. At 1st glance: are you sure about calling 

&F0($t1,@c);
...
&F0(($t2+$step/2),( @c + (&k1($t2)/2)));

[download]

? What (how many) arguments do you think F0 receives in each case?

Further, k2_1 calls k1. Just for sake of symmetry, I wonder if it should have been k1_1. Have you tested/debugged each subroutine/section, so they work as expected, instead of typing this huge and complex code to observe final results? And I suspect other monks' advice about code and PBP will follow.

In reply to Re: RK4 for a vectorial function by vr
in thread RK4 for a vectorial function by Lucero

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