251fad28-9f1c-4abf-8631-e595081ada48 8 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Option : the RK solving is given otherwise , generally from source or from user experiment.

In this example, RK Fixed renders better. It takes much higher number of steps ... not so "optimised" but useless. Still, the adaptive method works as due, supporting user "f" solving argument.

f 8 x 1 el * - 8 x 2 el * + 30 x 1 el * x 1 el + x 1 el x 3 el * - x 1 el x 2 el * 83 / x 3 el * - 31 mat :

<= conventionalise the RK solving argument t x D f :

Cauchy initial conditions x 10031 mat :

t 1 el 0 : start point ≡ T 10 : segment length ≡ ε 104 -^: accuracy ≡ h 0.01 : step size ≡ 41 line

j t 1 el h + : j T t 1 el + h + ≤ j j h + : tx x x cols col : k1 h 3 / j tx D eval * : k2 h 3 / j h 3 / + tx k1 + D eval * : k3 h 3 / j h 3 / + tx k1 k2 + 2 / + D eval * : k4 h 3 / j h 2 / + tx 3 k1 * 9 k3 * + 8 / + D eval * : k5 h 3 / j h + tx 3 k1 * 9 k3 * - 2 / + 6 k4 * + D eval * : δ k1 92 / k3 * - 4 k4 * + 12 / k5 * - : δ min abs 5 ε * ≤ (δ max abs 5 ε * ≤ (& x x tx 12 / k1 4 k4 * + k5 + (* + augment : steps 1 x cols el j : h h 2 * : 31 line j j h - : h h 2 / : 21 line if 81 line for

result steps x stack :

Number of values result cols 680

Y x # row transpose ≡ the Y collection ≡

X steps transpose : RK_1 X x 1 row transpose augment : RK_2 X x 2 row transpose augment : RK_3 X x 3 row transpose augment : 41 line

result 0 0.01 0.03 0.05 0.07 0.09 0.11 0.13 0.15 1 0.935 0.884 0.922 1.039 1.235 1.516 1.894 2.39 0 0.299 0.858 1.413 2.016 2.715 3.559 4.602 5.906 0 0.001 0.012 0.031 0.062 0.111 0.189 0.314 0.516 49 mat

Discrete export of solution(s).

RK_1 RK_2 RK_3 3 1 sys RK_2 2 col RK_3 2 col augment