80e2596a-3abc-42aa-ba84-6eb68cc38645 33 3 5 decimal

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X1 0 : X2 1 : N 100 : K 0.005 : TMAX 0.5 : 15 mat

W = 1 implicit
W = 0.5 Crank W 1 :

Functions used in conditions T P 0 ≡ T Q 0 ≡ X F 100 π X * sin * : 31 sys

Ω A 1 el 0 : B 1 el 0 : C 1 el 0 : D 1 el 0 : T 1 el 0 : 15 mat H X2 X1 - N / : R K H 2^/ : i 1 N range X i 1 + el X1 i H * + : U i 1 + el X i 1 + el F : 21 line for L N 1 - : TMAX T - abs K 2 / ≥ i 1 L range A i 1 + el W R * - : B i 1 + el 12 W * R * (+ : C i 1 + el W R * - : D i 1 + el U i 1 + el 1 W - (R * U i el 2 U i 1 + el * - U i 2 + el + (* + : 41 line for i 2 L range RT i 1 + el A i 1 + el - B i el / : B i 1 + el B i 1 + el RT i 1 + el C i el * + : D i 1 + el D i 1 + el RT i 1 + el D i el * + : D i 1 + el D i 1 + el B i 1 + el / : 41 line for i L 1 - (1 L 2 - (range D i 1 + el D i 1 + el C i 1 + el D i 2 + el * (- B i 1 + el / : for T T K + : i 1 L range U i 1 + el D i 1 + el : for U 1 el 0 : U N 1 + el 0 : 71 line while X U augment 71 line eval :

PDEsolve . . .

Adapted Mathcad 11 [id FORTRAN].

As is, not more exercised.

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t K : x 01 X2 X1 - N / range : t x exact 100 π 2^t * - exp * π x * sin * : 31 sys

EX t x exact vectorize :

sol Ω EX augment :

sol 1 col sol 2 col augment sol 1 col sol 3 col augment 2 1 sys

sol 000 0.01 3.141 2.99 0.02 6.279 5.977 0.03 9.411 8.958 0.04 12.533 11.93 0.05 15.643 14.89 0.06 18.738 17.836 0.07 21.814 20.764 0.08 24.869 23.672 0.09 27.899 26.556 103 mat

Partial Differential Equation x t u t diff x t u x 2 diff - 0 ≡

Subject to the following conditions x 0 u 100 π x * sin * ≡ 0 t u 0 ≡ 1 t u 0 ≡ 31 sys

Known solution 100 π 2^t * - exp * π x * sin *