Vrkfixed(y0,t0,t2,N,f)

64b7e9e9-577f-42d4-8cf7-66e8752858c3 15 4 5 decimal

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

y0 t0 t2 N f Vrkfixed t 1 el t0 : Y 1 el y0 : Δ t2 t0 - N / : 13 mat i 2 N range k1 t i 1 - el Y i 1 - el f Δ * eval break try : k2 t i 1 - el Δ 2 / + Y i 1 - el k1 2 / + f Δ * eval break try : k3 t i 1 - el Δ 2 / + Y i 1 - el k2 2 / + f Δ * eval break try : k4 t i 1 - el Δ + Y i 1 - el k3 + f Δ * eval break try : Y i el Y i 1 - el 16 / k1 2 k2 * + 2 k3 * + k4 + (* + : t i el t i 1 - el Δ + : 61 line for t Y augment 31 line :

Smath 1/1 Valery MCD ... ~ mwode113

t Y f t Y 1 el (3.5^^t Y 2 el (1^^+ t Y 1 el (2^^t Y 2 el (0.25^^+ 21 mat :

t0 0 : t2 2 : N 1000 : 31 line

y0 0.5 121 mat :

[t2, N} govern Δ
reflexive wrt plots Δ t2 t0 - N / : 0.002

Nested solutions
Range 'U'
Isolate 'U' explode rkfΔ y0 t0 t2 N f Vrkfixed : j 1 rkfΔ rows range : U rkfΔ j 2 el j el : 31 sys

j 1 rkfΔ rows range sol_1 j el U j 1 el 1 el : for

j 1 rkfΔ rows range sol_2 j el U j 1 el 2 el : for

rkfΔ 0 0.5 121 mat 0.002 0.501 121 mat 0.004 0.502 1.001 21 mat 0.006 0.503 1.001 21 mat 0.008 0.505 1.002 21 mat 0.01 0.506 1.003 21 mat 0.012 0.507 1.003 21 mat 0.014 0.509 1.004 21 mat 0.016 0.51 1.005 21 mat 0.018 0.511 1.005 21 mat 0.02 0.513 1.006 21 mat 0.022 0.514 1.007 21 mat 122 mat

Compactum ...
"Unest" route works well
much slower, not offered. sol rkfΔ 1 col sol_1 sol_2 augment : sol sol : SOL_1 sol 1 col sol 2 col augment : SOL_2 sol 1 col sol 3 col augment : 41 sys

sol sol rows row 1.18 5.2013 2.5372 13 mat

jnct 1.18 2.5372 augment :

sol 0 0.5 1 0.002 0.5009 1.0003 0.004 0.5021 1.0008 0.006 0.5034 1.0013 0.008 0.5046 1.0019 0.01 0.506 1.0025 0.012 0.5073 1.0032 0.014 0.5087 1.0038 0.016 0.51 1.0045 0.018 0.5114 1.0053 103 mat

SOL_1 SOL_2 jnct 3 1 sys MCD code

Piecewise sanity solved

Piecewise for upper  accuracy t x f t x 1 el (3.5^^t x 2 el (1^^+ t x 1 el (2^^t x 2 el (0.25^^+ 21 mat :

t0 0 : t1 1 : N 1000 : 31 line

IC 0.5 121 mat :

sol IC t0 t1 N t x f mwode113 :

X sol 1 col : discretised variable of integration ≡ sol_1 X sol 2 col augment : function ≡ sol_2 X sol 3 col augment : 1rst derivative ≡ 31 line

sol_1 sol_2 2 1 sys

t0 1 : t1 2 : N 1000 : 31 line

next sol sol rows row : 1 1.57341 2.075217 13 mat

IC next 12 el next 13 el 21 mat : 1.57341 2.075217 21 mat

Division by zero Sol IC t0 t1 N t x f mwode113 :

X Sol 1 col : Sol_1 X Sol 2 col augment : Sol_2 X Sol 3 col augment : 31 line

sol_1 sol_2 Sol_1 Sol_2 1 5 1 0 2 2 mat 5 1 sys

On the importance of origin vs balistic end solution

t0 01012 -^21 mat ≡

t0 0 : t1 2 : N 1000 : 31 line

v 0.5 121 mat :

solOne 0.5 121 mat t0 t1 N t x f mwode113 :

solOne solOne rows row 1.178 2.581198 2.527765 13 mat