plotG(vx,vy,a,b,c)

b2d19d9c-e59a-46e8-8b19-ba3755f0ee53 15 4 5 decimal

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

plotG(vx,vy,a,b,c)

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

D1(t,θ) ... DE from source

x y D1 6 y - 546918 x * + log10 * + (* + (* 312500000000567566 y + 34518 x * + log10 * + (* 29334518 x * + log10 * + (2^273 y + (2^+ (* + (* 3925500100425000773 y * + (* 169 y 2^* - (* 111 y 3^* + (* / :

Part 1: Interpolate/Extrapolate/Solve

x y f x y D1 :

Smath rkf45 . . . is essentially an open style rk

. . . integrator designed for immediate integration @ user input.

All ODE's work on the same principle @ close rkf45 acuracy.

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Dummies to enable
rkf45 for in-situ X 0 : Y 0 : h 0 : 13 mat

00 f 0.5237

rkf45 Compactum

fhelberg companion in compactum format given as point compute/integrate X Y h fehlberg k1 h X Y f (* eval : k2 h X 14 / h * + Y 14 / k1 * + f * eval : k3 h X 38 / h * + Y 332 / k1 * + 932 / k2 * + f * eval : k4 h X 1213 / h * + Y 19322197 / k1 * + 72002197 / k2 * - 72962197 / k3 * + f * eval : k5 h X h + Y 439216 / k1 * + 8 k2 * - 3680513 / k3 * + 8454104 / k4 * - f * eval : k6 h X h 2 / + Y 827 / k1 * - 2 k2 * + 35442565 / k3 * - 18594104 / k4 * + 1140 / k5 * - f * eval : out X h + Y 25216 / k1 * 14082565 / k3 * + 21974104 / k4 * + k5 5 / - (+ Y 16135 / k1 * 665612825 / k3 * + 2856156430 / k4 * + 950 / k5 * - 255 / k6 * + (+ k1 360 / 1284275 / k3 * - 219775240 / k4 * - k5 50 / + 255 / k6 * + 41 mat : 71 line :

k1 h X Y f (* eval : k2 h X 14 / h * + Y 14 / k1 * + f * eval : k3 h X 38 / h * + Y 332 / k1 * + 932 / k2 * + f * eval : k4 h X 1213 / h * + Y 19322197 / k1 * + 72002197 / k2 * - 72962197 / k3 * + f * eval : k5 h X h + Y 439216 / k1 * + 8 k2 * - 3680513 / k3 * + 8454104 / k4 * - f * eval : k6 h X h 2 / + Y 827 / k1 * - 2 k2 * + 35442565 / k3 * - 18594104 / k4 * + 1140 / k5 * - f * eval : 61 line

out X h + Y 25216 / k1 * 14082565 / k3 * + 21974104 / k4 * + k5 5 / - (+ eval Y 16135 / k1 * 665612825 / k3 * + 2856156430 / k4 * + 950 / k5 * - 255 / k6 * + (+ eval k1 360 / 1284275 / k3 * - 219775240 / k4 * - k5 50 / + 255 / k6 * + eval 41 mat :

out 000041 mat

k1 k2 k3 k4 k5 k6 61 mat X Y h fehlberg 12 mat 00000061 mat 000041 mat 12 mat

extrapolate 003 fehlberg 3 45.44 45.42 0.01 - 41 mat

interpolate 001 π / fehlberg 0.31831 1.274892 1.274712 0.00018 - 41 mat

Part 2: Range/Populate/Export

collect/populate the 'n' integrate values from fehlberg  algo init x0 x1 n RKF45 j 1 n 1 + (range h j el 1 - j + n / : for sol will be nested colwise j 1 h rows range sol 1 j el init x0 x1 h j el (* fehlberg : for Unest sol U sol 1 el : j 2 sol cols range U U sol j el augment : for U transpose 71 line :

RKF45 00630 RKF45 :

vx RKF45 1 col (: (collect variate 'x' ≡ vy RKF45 3 col (: (collect rkf45 solut'n ≡ XY vx vy augment : (export data solut'n ≡ 31 line

XY 00 0.2 0.59 0.4 1.86 0.6 3.62 0.8 5.78 1 8.27 1.2 11.06 1.4 14.1 1.6 17.39 1.8 20.88 2 24.58 2.2 28.44 2.4 32.47 2.6 36.66 2.8 40.98 3 45.42 162 mat

vx vy . 12 black plotG

x λ 10 x ≤ (cases :

x Lin vy vx x linterp :

r 4 :

S x Lin r - x 0120 solve : 69.27

S 10 S 2 - 2 2 mat x Lin x λ * 16 - r S r 2 2 mat vy vx . 12 black plotG 4 1 sys

R1 00530 t θ D1 Rkadapt :

R1 R1 rows row 5 96.53 12 mat

005 fehlberg 5 95.06 95.11 0.05 41 mat

relative error at end point 1 96.53 95.06 / - % / 1.55 -

M 00530 t θ D1 mwode113 :

M M rows row 5 96.53 12 mat