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Dragilev parametric method ... extended Ber7 20181029

Draghilev method n = 2, α-parameter 2 f X0 tmin tmax N D J ξ 1 el ξ 2 el f ξ 1 el diff ξ 1 el ξ 2 el f ξ 2 el diff 12 mat : t ξ D J 12 el - J 11 el 12 mat transpose J transpose 1 el (2^J transpose 2 el (2^+ sqrt / : X0 tmin tmax N t ξ D rkfixed 31 line : x0 α X0 x0 x0 y f zoom α * - 0 ≡ y solve maple 1 el eval 21 mat : x0 α B x y f x0 eval α X0 tmin tmax N D : 31 line

x y f x 4^2 x 2^* y * + 3 x * y 2^* - y 3^+ :

Δt 0.025 :

tmax 5 :

tmin 0 :

x0 0.94 :

N 200 :

zoom 0.05 :

Plot α 05 range con α 1 + el x0 α B 2 col x0 α B 3 col augment : for con mat2sys.1 21 line :

t0 1 time :

con mat2sys.1 collect plot as single argument ≡

The parametrization Human eye by Draghilev method

Plot

1 time t0 - 46 s *

Dragilev method for equations with a parameter

Draghilev method n = 2, α-parameter 2 f X0 tmin tmax N D J ξ 1 el ξ 2 el f ξ 1 el diff ξ 1 el ξ 2 el f ξ 2 el diff 12 mat : t ξ D J 12 el - J 11 el 12 mat transpose J transpose 1 el (2^J transpose 2 el (2^+ sqrt / : X0 tmin tmax N t ξ D rkfixed 31 line : x0 α X0 x0 x0 y f zoom α * - 0 ≡ y solve eval 21 mat : x0 α B x y f x0 eval α X0 tmin tmax tmax Δt / D : 31 line

t0 1 time :

Δt 0.025 : tmax 5 : tmin 0 : x0 0.94 : zoom 0.05 : 51 sys

x y f x 4^2 x 2^* y * + 3 x * y 2^* - y 3^+ :

Plot α 05 range con α 1 + el x0 α B 2 col x0 α B 3 col augment eval : for con mat2sys.1 21 line :

The parametrization Human eye by Draghilev method

Plot

1 time t0 - 36 s *

con mat2sys.1 collect plot as single argument ≡

Draghilev method n = 2, α-parameter ... collapse as a master Smath function 2 f X0 tmin tmax N D J ξ 1 el ξ 2 el f ξ 1 el diff ξ 1 el ξ 2 el f ξ 2 el diff 12 mat : t ξ D J 12 el - J 11 el 12 mat transpose J transpose 1 el (2^J transpose 2 el (2^+ sqrt / : X0 tmin tmax N t ξ D dn_GearsBDF 31 line : x0 α X0 x0 x0 y f zoom α * - 0 ≡ y solve eval 21 mat : x0 α B x y f x0 eval α X0 tmin tmax tmax Δt / D : 31 line

Δt 0.01 : tmax 5 : tmin 0 : x0 1 : zoom 0.05 : 51 sys

x y f x 4^2 x 2^* y * + 3 x * y 2^* - y 3^+ :

t0 1 time :

Plot α 05 range con α 1 + el x0 α B 2 col x0 α B 3 col augment eval : for con mat2sys.1 21 line :

The parametrization Human eye by Draghilev method

Plot

1 time t0 - 13 s *

3 appVersion 0.98.6179 ≡ WS_timing ~ 1.5 min ≡ 21 mat

method ..... solver ........ N ... time (s) ... loop[0] ...... remark

--------------------------------------------------------------------------

maple........ rkfixed .......200 ... 45 ...........visible ......... x0 [0.94]

solve ........ rkfixed ...... 200 ... 36 .......... visible ......... x0 [0.94]

solve ....... GearsBDF 500 ... 13 .......... NO ............. x0 [1]

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