Integrating error: maximum number of subdivisions reached

numerical-integration, plot, r

Solution

The algorithm is not converging before 100 subdivisions are exceeded. You can increase the number of allowed subdivisions, or increase the tolerance:

More allowed subdivisions:

f_fourier <- function(X) {
    Y <- sapply(X, function(x) {
        integrand <- function(l) {
            y <- (2 / pi) * cos(l * x) / (l^2 + 1)
        }
        integrate(integrand, lower = 0, upper = Inf, subdivisions=2000)$value
    })
}

plot(f_fourier(X))

Increased tolerance:

f_fourier <- function(X) {
    Y <- sapply(X, function(x) {
        integrand <- function(l) {
            y <- (2 / pi) * cos(l * x) / (l^2 + 1)
        }
        integrate(integrand, lower = 0, upper = Inf, rel.tol=.Machine$double.eps^.05)$value
    })
}

plot(f_fourier(X))

Problem

I am trying to plot a Fourier integral, but I get error while integrating ``` X <- seq(-10, 10, by = 0.05) f_fourier <- function(X) { Y <- sapply(X, function(x) { integrand <- function(l) { y <- (2 / pi) * cos(l * x) / (l^2 + 1) } integrate(integrand, lower = 0, upper = Inf)$value }) } plot(X,f_fourier(X)) ``` Error: ``` maximum number of subdivisions reached ``` I found out that "cos(l * x)" causes this error but Wolfram gives me normal result. Can you suggest something?

Original source