<content> <p>3d Draghilev method</p> </content>

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γ 0.8232 - 0.4194 - 0.3827 0.5677 0.6187 - 0.543 0.009 0.6643 0.7474 33 mat :

3d Draghilev  method x0 tmax Δt D f x f : n f length 1 + : c 1 n range : u c el x c el : x J f u Jacobian : 15 mat b x J 1 n 1 - n n submatrix - : A x J 1 n 1 - 1 n 1 - submatrix : V b 1 el A det 12 mat transpose f rows 1 ≡ b A 1222 submatrix augment det A 1211 submatrix b augment det A det 31 mat - cases : X0 x0 x f al_nleqsolve : N tmax Δt / : t x v V V norme / : 13 mat X0 0 tmax N t x v rkfixed 1 N 2 n 1 + submatrix 61 line :

x f 2 π * x 1 el x 2 el + 2 x 3 el * - (* cos 2 π * x 2 el x 3 el + 2 x 1 el * - (* cos + 2 π * x 3 el x 1 el + 2 x 2 el * - (* cos + x 3 el 0.7 - 21 mat :

x0 0.3 0.5 0.7 13 mat transpose : Δt 0.01 : tmax 1.4 : 13 mat

B x0 tmax Δt D :

k 1 B rows range ε k el B k row f : 11 line for

B γ * 20 *

ε 6.0839 1010 -^* - 1.84 1012 -^* - 21 mat 2.4965 108 -^* - 1.84 1012 -^* - 21 mat 3.345 108 -^* - 1.84 1012 -^* - 21 mat 3.3599 108 -^* - 1.84 1012 -^* - 21 mat 3.1582 108 -^* - 1.84 1012 -^* - 21 mat 3.0639 108 -^* - 1.84 1012 -^* - 21 mat 3.1694 108 -^* - 1.84 1012 -^* - 21 mat 3.4511 108 -^* - 1.84 1012 -^* - 21 mat 81 mat

B 0.2532 0.5019 0.7 0.2548 0.492 0.7 0.2555 0.482 0.7 0.2554 0.472 0.7 0.2547 0.4621 0.7 0.2534 0.4522 0.7 0.2515 0.4423 0.7 0.2492 0.4326 0.7 0.2465 0.423 0.7 0.2435 0.4135 0.7 0.2401 0.404 0.7 0.2364 0.3947 0.7 0.2325 0.3855 0.7 0.2284 0.3764 0.7 0.2241 0.3674 0.7 0.2195 0.3585 0.7 0.2148 0.3497 0.7 0.2098 0.341 0.7 0.2047 0.3324 0.7 0.1993 0.324 0.7 0.1938 0.3156 0.7 0.1881 0.3074 0.7 0.1823 0.2993 0.7 233 mat