Numerical Differentiation

Universitas : UIN Maulana Malik Ibrahim Malang

Prodi : Teknik Informatika

Fakultas : Sains dan Teknologi

Dosen : Prof. Dr. SUHARTONO, M.Kom

Numerical Differentiation

Introduction

Numerical differentiation is a technique to approximate derivatives of functions when an analytical expression for the derivative is not available.

Finite Difference Method

# Function for which we want to find the derivative
f <- function(x) x^2 + 2*x + 1

# Finite difference method for numerical differentiation
finite_difference <- function(f, x, h = 1e-6) {
  (f(x + h) - f(x)) / h
}
# Point at which to find the derivative
x_value <- 2

# Compute the numerical derivative


numerical_derivative <- finite_difference(f, x_value)

numerical_derivative

## [1] 6.000001

Central Difference

Central difference method for numerical differentiation

central_difference <- function(f, x, h = 1e-6) {
  (f(x + h) - f(x - h)) / (2 * h)
}

# Compute the numerical derivative using central difference
numerical_derivative_central <- central_difference(f, x_value)

numerical_derivative_central

## [1] 6