Zadanie:

Zo slajdov:

Riešenie PDR pre \(v(x,t)\)

\[f_k(t) = B_k \sin(t) + (B_k-A_k) \cos(t)\]

riesenie <- function(x,t){ # x = cislo (nie vektor)
N <- 20
k <- 1:N
a <- 1

Ak <- (2 - 2*(-1)^k)/(k * pi)
Bk <- 2 * (-1)^(k+1)/(k * pi)

Mk <- (-(Bk-Ak) - Bk * k^2 * pi^2 * a^2)/(-1 - k^4*pi^4*a^4)

Nk <- (Bk - k^2 * a^2 * pi^2 * (Bk - Ak))/(-1 - k^4 * pi^4 * a^4)

Ck <- (-Nk)

alpha_k <- Ck * exp(-k^2 * a^2 * pi^2*t) + Mk * sin(t) + Nk * cos(t)

v <- sum(alpha_k * sin(k*pi*x))
u <- v + sin(t) + x * (cos(t) - sin(t))
return(u)
}
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