<p> Mathcad Valery </p>

fb63b451-ba19-46cb-9812-78d102dfd996 8 4 5 decimal

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

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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 :

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 :

ε 1015 -^:

t0 0 : t2 1.5 : N 250 : 31 line

Does NOT support '0' y0 ε 121 mat :

From recollection, one of the 17 Smath ODE solves this difficult system ... Which one ? This example is 1/1 Mathcad 11 Valery.

sol y0 t0 t2 N f Vrkfixed :

unest the system j 1 sol rows range : U sol j 2 el j el : 21 sys

sol 011015 -^* 121 mat 0.006 0.005 1.005 21 mat 0.012 0.0111 1.0111 21 mat 0.018 0.0172 1.0172 21 mat 0.024 0.0233 1.0233 21 mat 0.03 0.0294 1.0294 21 mat 0.036 0.0356 1.0356 21 mat 0.042 0.0418 1.0418 21 mat 82 mat

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

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

Explode2sols

U 11015 -^* 121 mat 0.005 1.005 21 mat 0.0111 1.0111 21 mat 0.0172 1.0172 21 mat 0.0233 1.0233 21 mat 0.0294 1.0294 21 mat 0.0356 1.0356 21 mat 0.0418 1.0418 21 mat 0.048 1.048 21 mat 0.0543 1.0543 21 mat 0.0606 1.0605 21 mat 111 mat

Export system sol sol 1 col sol_1 sol_2 augment :

plot sol 1 col sol_1 augment sol 1 col sol_2 augment 21 sys :

sol 011015 -^* 1 0.006 0.005 1.005 0.012 0.0111 1.0111 0.018 0.0172 1.0172 0.024 0.0233 1.0233 53 mat

plot 1.224 2 1.224 1 - 2 2 mat 2 1 sys

plot 2 el plot 2 el rows row 1.224 2.922 12 mat

<p> Mathcad Valery </p>