<p> plot(data,a,b,c) </p>

0e555a4e-fd27-4774-8189-c3584e377a36 15 4 5 decimal

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

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

Radau Polynomials @ accuracy of solve(■,■,■,■)

Legendre  setup 6179 needs "local assignment" n x L 1 - (k^2 n * 2 k * - (! (x n 2 k * -^* (* 2 n^k! (* n k - (! (n 2 k * - (! (* (* / (k 0 n 2 / Floor sum 11 line :

x λ 11 - x ≤ (x 1 ≤ (& cases :

n x Radau n 1 - x L n x L + x 1 + / :

n 10 :

Plot roots of Radau r n x Radau x 1 - 1 solve : r r eval : roots r r 0 * augment : roots roots . 14 black plot : 41 line

r 0.9275 - 0.7638 - 0.5256 - 0.2362 - 0.0761 0.3807 0.6478 0.8512 0.9712 91 mat

Radau ODE solver was introduced in Mathcad 11 ... NO code found. HIRES application ~ = Rkadapt.

roots n x Radau x λ * 2 1 sys

r 1 - r stack (:

i 1 r rows range W i el 1 n 2^/ 1 r i el - (n 1 - r i el L (2^/ * : Wr r W augment : 21 line for

Sanity MCD 11
F.B. Hildebrand Wr 1 - 0.02 0.9275 - 0.1203 0.7638 - 0.2043 0.5256 - 0.2682 0.2362 - 0.3059 0.0761 0.3136 0.3807 0.2906 0.6478 0.2392 0.8512 0.1644 0.9712 0.0738 102 mat

x f x 1 - 1 int 2 n 2^/ 1 - f * W i el x i el f * i 0 n 1 - sum * ≡

Legendre  setup 6179 needs "local assignment" n x L 1 - (k^2 n * 2 k * - (! (x n 2 k * -^* (* 2 n^k! (* n k - (! (n 2 k * - (! (* (* / (k 0 n 2 / Floor sum 11 line :

Radau explorer ... Export

n x Radau n 1 - x L n x L + x 1 + / :

j 10 : n 1 j range Rad n el n x Radau : for 21 line

select/collect Rad 3 el 1 x 2^35 x * + (* - 3 x * + 21 x + (* / -

eval SYMBOLIC view all x Radau Rad :

x λ 11 - x ≤ (x 1 ≤ (& cases :

j 10 :

ρoots x Radau j el x 1 - 1 solve : ρoots ρoots eval : roots ρoots ρoots 0 * augment : roots roots . 14 black plot : 41 line

roots x Radau j el x λ * 1 2 1 2 - 2 2 mat 3 1 sys

ρoots 0.9275 - 0.7638 - 0.5256 - 0.2362 - 0.0761 0.3807 0.6478 0.8512 0.9712 91 mat