The thing that strikes me as particularly weird about this is the use of numpy there. In other languages, they're using native code. In python they're reaching out to numpy, which is a great library, but not awesome inside a hot loop unless you're keeping the operation you're carrying out within numpy itself. This means, right in that hot loop, they're doing a lot of translating of numbers between python representation and native c representation.

Cutting numpy out by making the line "t = [0.0]*l" gets it down to 17059 ms, without attempting any other optimisations. Using that plus pypy (so you get the JIT that you have with javascript/v8) gets it down to 958 ms.

To show the cost of those translations, sticking with numpy. If we switch that inner loop to:

        temp_t_i = t[i]
        temp_t_i += 0.02 * j
        temp_t_i *= 0.03 * j
        temp_t_i -= 0.04 * j
        temp_t_i /= 0.05 * (j+1)
        temp_t_i = temp_t_i

It speeds us up from 47552 ms to 28251 ms. Almost half the execution time. That's still doing two hops back and forth, though. If you cut it down to a single line it's even faster at 18458 ms, cutting execution time down to about a third of the original example. Pypy isn't able to help here at all, this is sort of a pathological case for it.

edit: I'll add, I'm not that good with numpy, rarely use it myself. Not sure if it's possible to do that inner loop all within numpy somehow. I imagine that'd be a lot faster still.