<p> Stem(data) </p>

24cc3437-8eac-4fb2-ac52-f6bca84007ce 5 3 5 decimal

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

Rkadapt45 native and aqually spaced

f x 2 el 25 x 1 el * x 2 el + (* t sin - (- 21 mat :

t0 1 time :

<= conventionalise the RK solving argument t x D f :

Cauchy initial conditions
Y0, Y1 in Laplace solver IC 1021 mat :

t 1 el 0 : (start point ≡ T 10 : (segment length ≡ 21 line

ε 107 -^: (accuracy ≡ h 0.05 : (step size ≡ 21 line

j t 1 el h + : j T t 1 el + h + ≤ j j h + : tx IC IC cols col : k1 h 3 / j tx D eval * : k2 h 3 / j h 3 / + tx k1 + D eval * : k3 h 3 / j h 3 / + tx k1 k2 + 2 / + D eval * : k4 h 3 / j h 2 / + tx 3 k1 * 9 k3 * + 8 / + D eval * : k5 h 3 / j h + tx 3 k1 * 9 k3 * - 2 / + 6 k4 * + D eval * : δ k1 92 / k3 * - 4 k4 * + 12 / k5 * - : δ min abs 5 ε * ≤ (δ max abs 5 ε * ≤ (& IC IC tx 12 / k1 4 k4 * + k5 + (* + augment : steps 1 IC cols el j : h h 2 * : 31 line j j h - : h h 2 / : 21 line if 81 line for

4 appVersion 0.98.6179.21440 ≡ Timing 45 sec ≡ 21 mat

<= from for-loop result steps IC stack :

Number of values result cols 215

Prepare/extract solutions

the 'x' direction
.....
the fnct solution
.....
the derivative X steps transpose : RK_1 X IC 1 row transpose augment : RK_2 X IC 2 row transpose augment : 31 sys

result 0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 1 0.997 0.988 0.973 0.954 0.929 0.901 0.868 0 0.243 - 0.471 - 0.686 - 0.884 - 1.068 - 1.235 - 1.386 - 38 mat

Discrete unequally spaced solutions.

RK_1 RK_2 2 1 sys

x sol_1 0 x ≤ (x T ≤ (& RK_1 1 col RK_1 2 col x cinterp out range if :

x sol_2 0 x ≤ (x T ≤ (& RK_2 1 col RK_2 2 col x cinterp out range if :

Fine meshing over the canvas plot.

x sol_1 x sol_2 2 1 sys

Laplace Analytic

Stem construction over a data set data Stem stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

space j 2 result cols range idx j el j : δ j el result 1 j el result 1 j 1 - el - : 21 line for idx δ augment 21 line :

Te RK5 adaptive space observer

space 2 col Max space 2 col Min 21 mat 0.1 021 mat

space Stem 0 0.025 + 50 red 1 5 mat 50 0.05 + 150 red 1 5 mat 175 0.1 + 275 red 1 5 mat 4 1 sys

Export equally spaced solutions

1 time t0 - 36 s *

L H N xd U 0 : dx H L - N / : 12 mat i 1 N 1 + (range U i el L dx - (dx i * + eval : for U 31 line :

L 0 : H 10 : N 500 : 13 mat u L H N xd : 21 sys

x U_1 RK_1 1 col RK_1 2 col x cinterp : x U_2 RK_2 1 col RK_2 2 col x cinterp : 21 sys

U1 n 1 u rows range u1 n el u n el U_1 eval : for u u1 augment 21 line :

U2 n 1 u rows range u2 n el u n el U_2 eval : for u u2 augment 21 line :

U1 U2 2 1 sys

OBSERVE . . . U_1(x), U_2(x)

interpolate on the canvas and on command.

They must be passed to program module to

produce the desired = spaced export.

This transit is fast [cinterp is native fast].

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1 time t0 - 48 s *