Oui

open Printf

(*Création du tableau RK4 composé de
tau, b et a comme vu au cours *)

let tau = [|0.;0.5;0.5;1.|]

let b = [|1./.6.;1./.3.;1./.3.;1./.6.|]

let a = [|[||];
        [|0.5|];
        [|0.;0.5|];
        [|0.;0.;1.|]|]

(*Multiplication d'un tableau par un float k*)
let mult k a = Array.map (fun i -> k*.i) a

(*Addition de 2 tableaux de même taille*)
let add a1 a2 =
    if a1 = [||] then
        a2
    else if a2 = [||] then
        a1
        else
            let arr = Array.make (Array.length a1) 0. in
            for i = 0 to (Array.length a1)-1 do
                arr.(i) <- a1.(i) +. a2.(i)
            done;
            arr
(*évaluation de f au temps t*)
let rk4 f u t n =
    let k = Array.make 4 [||] and
    h = t/. float_of_int n and
    u_i = ref u in
    let t_i = ref 0. in
    for i = 0 to n do
        (*calcul des k_j*)
        k.(0) <- mult h (f (!t_i +. tau.(0) *. h) !u_i);
        for j = 1 to 3 do
            let res = ref [||] in
            (*somme des vecteurs a_jl*k_l quand l < j*)
            for l = 0 to j-1 do
                res := add !res (mult a.(j).(l) k.(l))
            done;
                res := add !u_i !res;
                k.(j) <- mult h (f (!t_i +. tau.(j) *. h) !res);
        done;
        (*Somme de b_j*k_j*)
        let tmp = ref [||] in
        for j = 0 to 3 do
            tmp := add !tmp (mult b.(j) k.(j))
        done;
        u_i := add !u_i !tmp;
        t_i := !t_i +. h;
        (* printf "ui1: %g ui2: %g\n" !u_i.(0) !u_i.(1) *)
    done;
    !u_i