468632a3-bb29-4c68-bb91-980c8136256f 174 Вячеслав Мезенцев 4 5 false false false 0 0 decimal

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

Using the prompt SMathAI.md on https://aistudio.google.com/

# # F t0 Y0 t_end h_initial tol RK4A h h_initial : t t0 : Y Y0 : Results t 11 mat Y transpose augment : t t_end < h t h + t_end > t_end t - h if : h_half h 2 / : k1 h t Y F * : k2 h t h 2 / + Y k1 2 / + F * : k3 h t h 2 / + Y k2 2 / + F * : k4 h t h + Y k3 + F * : Y_one_step Y k1 2 k2 * + 2 k3 * + k4 + (6 / + : k1a h_half t Y F * : k2a h_half t h_half + Y k1a 2 / + F * : k3a h_half t h_half + Y k2a 2 / + F * : k4a h_half t h_half + Y k3a + F * : Y_mid Y k1a 2 k2a * + 2 k3a * + k4a + (6 / + : k1b h_half t h_half + Y_mid F * : k2b h_half t h_half + h_half 2 / + Y_mid k1b 2 / + F * : k3b h_half t h_half + h_half 2 / + Y_mid k2b 2 / + F * : k4b h_half t h_half + h_half + Y_mid k3b + F * : Y_two_steps Y_mid k1b 2 k2b * + 2 k3b * + k4b + (6 / + : Error Y_two_steps Y_one_step - norme 15 / : Error Error 1012 - (^< tol Error if : t t h + : Y Y_two_steps : Results Results t 11 mat Y transpose augment stack : h 0.9 h * tol Error / (15 / (^* : 231 line while Results 61 line :

α:1.1
β:0.4
δ:0.1
γ:0.4
F(t,Y):mat(α*el(Y,1)-β*el(Y,1)*el(Y,2),δ*el(Y,1)*el(Y,2)-γ*el(Y,2),2,1)
t_initial:0
Y_initial:mat(20,5,2,1)
t_final:100
h_start:0.1
tolerance:0.001
solution:RK4A(F(t,Y),t_initial,Y_initial,t_final,h_start,tolerance)
solution=

α 1.1 :

β 0.4 :

δ 0.1 :

γ 0.4 :

t Y F α Y 1 el * β Y 1 el * Y 2 el * - δ Y 1 el * Y 2 el * γ Y 2 el * - 21 mat :

h_start 0.1 :

tolerance 0.001 :

Y_initial 20521 mat :

t_initial 0 :

t_final 100 :

M t Y F t_initial Y_initial t_final h_start tolerance RK4A : 0205 0.1 17.9854 5.8107 0.5096 8.5523 8.4581 0.8685 3.5596 9.0004 1.1692 1.7107 8.6067 1.5024 0.8233 7.8408 1.926 0.3804 6.7792 2.5162 0.173 5.4353 3.4646 0.0874 3.7615 5.0276 0.0839 2.0379 103 mat

M 1 col M 2 col augment M 1 col M 3 col augment

Alvaro

4 appVersion 1.73.9126.0