noah/CS-7863-Sci-Stat-Proj-3
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Adding central difference approx

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Adding plot title
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Noah L. Schrick 2023-02-14 17:33:31 -06:00
parent aa38089910
commit 2f9163eec2
1 changed files with 18 additions and 2 deletions
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Schrick-Noah_Homework-3.R
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@ -5,7 +5,7 @@
## 1. Approximate deriv. of sin(x) at x=pi from h=10^-1 -> 10^-20
forward.approx <- function(func, x, h){
approx <- (func(x+h) - func(x))/h
approx <- (func(x+h)-func(x))/h
}
forward.approx.table <- matrix(nrow = 0, ncol = 3)
@ -17,9 +17,25 @@ for(h in 10^(seq(-1,-20,-1))){
}
plot(abs(log(forward.approx.table[,"h"],10)), forward.approx.table[,"error"],
xlab="h [10^-x]", ylab="error (logscale)", type="o", log="y")
xlab="h [1e-x]", ylab="error (logscale)", type="o", log="y",
main = "Forward Approximation of sin(x) at x=pi")
# Repeat with central difference approx
central.diff.approx <- function(func, x, h){
approx <- (func(x+h)-func(x-h))/(2*h)
}
central.diff.table <- matrix(nrow = 0, ncol = 3)
colnames(central.diff.table) <- c("h", "approximation", "error")
for(h in 10^(seq(-1,-20,-1))){
approx <- central.diff.approx(sin, pi, h)
error <- abs(cos(pi)-approx)
central.diff.table <- rbind(central.diff.table, c(h, approx, error))
}
plot(abs(log(central.diff.table[,"h"],10)), central.diff.table[,"error"],
xlab="h [1e-x]", ylab="error (logscale)", type="o", log="y",
main = "Central Difference Approximation of sin(x) at x=pi")
## 2.
# a) Runge-Kutta