PDE HW 1

PDE Assignment 1 Lila Juenger C)

u <- function(x, t) {
  ((-1 + sqrt(1 + 8*t*x)) / (4*t))^2
}

x <- seq(0, 2, length.out = 200)

plot(x, u(x, 1), type = "l", lwd = 2,
     xlab = "x", ylab = "u(x,t)",
     main = "u(x,t) vs x")

lines(x, u(x, 2), lwd = 2, lty = 2)

legend("topright", legend = c("t = 1", "t = 2"),
       lty = c(1,2), lwd = 2)

t <- seq(0.1, 2, length.out = 200)  

plot(t, u(0, t), type = "l", lwd = 2,
     xlab = "t", ylab = "u(x,t)",
     main = "u(x,t) vs t")

lines(t, u(1, t), lwd = 2, lty = 2)

legend("topright", legend = c("x = 0", "x = 1"),
       lty = c(1,2), lwd = 2)