Sayısal İntegral (Numerical Integration / Quadrature) Algoritması

1// Yamuk Yöntemi
2function trapezoidRule(f: (x: number) => number, a: number, b: number, n: number): number {
3  const h = (b - a) / n;
4  let sum = 0.5 * (f(a) + f(b));
5  for (let i = 1; i < n; i++) { sum += f(a + i * h); }
6  return sum * h;
7}
8// Simpson Yöntemi
9function simpsonRule(f: (x: number) => number, a: number, b: number, n: number): number {
10  if (n % 2 !== 0) n++;
11  const h = (b - a) / n;
12  let sum = f(a) + f(b);
13  for (let i = 1; i < n; i++) { sum += (i % 2 === 0 ? 2 : 4) * f(a + i * h); }
14  return (sum * h) / 3;
15}
16// Romberg İntegrasyonu
17function rombergIntegration(f: (x: number) => number, a: number, b: number, steps: number): number {
18  const R: number[][] = Array.from({ length: steps }, () => Array(steps).fill(0));
19  R[0][0] = 0.5 * (b - a) * (f(a) + f(b));
20  for (let i = 1; i < steps; i++) {
21    const n = Math.pow(2, i), h = (b - a) / n;
22    let sum = 0;
23    for (let k = 1; k <= n; k += 2) { sum += f(a + k * h); }
24    R[i][0] = 0.5 * R[i-1][0] + sum * h;
25    for (let j = 1; j <= i; j++) { R[i][j] = R[i][j-1] + (R[i][j-1] - R[i-1][j-1]) / (Math.pow(4, j) - 1); }
26  }
27  return R[steps - 1][steps - 1];
28}