euler_method.ts

/**
 * @description Euler's method is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.
 * @param {number} x0 - The initial value of x
 * @param {number} y0 - The initial value of y
 * @param {number} h - The step size
 * @param {number} n - The number of iterations
 * @param {Function} f - The function
 * @return {number} - The value of y at x
 * @see [EulerMethod](https://en.wikipedia.org/wiki/Euler_method)
 * @example eulerMethod(0, 1, 0.1, 10, (x, y) => x + y) = 2.5937424601
 * @example eulerMethod(0, 1, 0.1, 10, (x, y) => x * y) = 1.7715614317
 */

export const eulerMethod = (
  x0: number,
  y0: number,
  h: number,
  n: number,
  f: Function
): number => {
  if (typeof f !== 'function') {
    throw new Error('f must be a function')
  }

  if (n < 0) {
    throw new Error('Number of iterations must be non-negative')
  }

  let x = x0
  let y = y0

  for (let i = 0; i < n; i++) {
    y = y + h * f(x, y)
    x = x + h
  }

  return y
}