<p> plotG(vx,vy,a,b,c) </p>

d83749e3-2459-46ca-8d8f-57b06ab05c02 13 4 5 decimal

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

Under "while", the module computes the last value(s). It can be used to interpolate on-line
and interpolate for a given vector. The project must be recast for other  Smath "RK".
Does NOT plot on canvas [not scalar] ... interpolate Rkadapt is defendable. init t1 t2 n f RK4 vx init : t t1 : h t2 t1 - n / : 13 mat t t2 < k1 t vx f h * eval : k2 t h 2 / + vx k1 2 / + f h * eval : 12 mat k3 t h 2 / + vx k2 2 / + f h * eval : k4 t h + vx k3 + f h * eval : 12 mat vx vx 16 / k1 2 k2 * + 2 k3 * + k4 + (* + eval : t t h + : 12 mat 31 line while vx 31 line :

===== Working a user system =====

x t f x t sqrt 0 + (+ :

mesh fine enough for smooth plot. init 0 : start 0 : end 2 : N 100 : 14 mat

last value @ 'end' ... sanity MCD 11 RK4 init start end N f RK4 : 3.9993

u SOL init start u N f RK4 start u ≤ (u end ≤ (& out range cases :

u 2.5 sqrt : 1.5811

1.23456789 SOL u SOL 21 mat 1.5239 2.4996 21 mat

<p> plotG(vx,vy,a,b,c) </p>

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 :

t0 1 time :

X 02 0.25 range : Y X SOL vectorize eval : XY X Y augment : x sol X Y x ainterp 0 x ≤ (x end ≤ (& out range cases : 41 sys

Notes :

1. Takes no time to interpolate @ user point(s), plot canvas.

2. This solver is identical to Mathsoft Odesolve, which by

same token does not rescue to spline interpolation. Rather it

is based on ¬ if IsScalar. The Odesolve block is a wraper of

fixed steps rk, adaptive, stiff from menu option.

Observe ========================

RK4(init,t1,t2,n,f) ... is sensibly more accurate than Smath

built-in rkfixed. On the other hand, Rkadapt is generally

not equally spaced for export. The proposal will adequately

interpolate from in-situ command.

]]>

U 0.6789 :

Ω U sol : 0.4608

track 0.5 - 313 U Ω 32 mat :

track x sol U U sol + 15 blue 1 5 mat X Y . 12 black plotG 4 1 sys

x t q x t sqrt 0 + (+ : t ω D t ω 1 el q : rkf 002 N t ω D rkfixed : rka 002 N t ω D Rkadapt : 41 sys

1 time t0 - 6.2 s *

Compare the 3 ODE solvers RK4 rkf rkf rows row rka rka rows row 31 mat 3.999 2 3.959 12 mat 2412 mat 31 mat

U Ω 12 mat 0.6789 0.4608 12 mat

Observe: "if/otherwise" does not interpolate 
on the canvas. "if/else" => slow but plots. x sol start x ≤ (x end ≤ (& init start x N f RK4 eval out range if :

t0 1 time :

user U 1.5 :

Ω U sol : 2.2496

x sol U Ω + 20 red 1 5 mat 2 1 sys

1 time t0 - min 1.7

U Ω 12 mat 1.5 2.25 12 mat

mesh at will your export X 02 0.1 range : Y X sol vectorize eval : XY X Y augment : 31 sys

XY 11 mat 00 0.1 0.01 0.2 0.04 0.3 0.09 0.4 0.16 0.5 0.25 0.6 0.3599 0.7 0.4899 0.8 0.6399 0.9 0.8099 1 0.9998 1.1 1.2098 1.2 1.4398 1.3 1.6897 1.4 1.9597 1.5 2.2496 1.6 2.5596 1.7 2.8895 1.8 3.2394 1.9 3.6094 2 3.9993 212 mat 11 mat

1 time t0 - min 1.9