https://github.com/rafifiaan/p2-numericalcomputation-py

Romberg Method - Numerical Computation Course
https://github.com/rafifiaan/p2-numericalcomputation-py

numerical-computation python rombergs-method

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Romberg Method - Numerical Computation Course

• Host: GitHub
• URL: https://github.com/rafifiaan/p2-numericalcomputation-py
• Owner: rafifiaan
• Created: 2022-12-08T14:09:54.000Z (over 2 years ago)
• Default Branch: main
• Last Pushed: 2022-12-08T15:27:23.000Z (over 2 years ago)
• Last Synced: 2025-02-25T20:18:25.637Z (4 months ago)
• Topics: numerical-computation, python, rombergs-method
• Language: Python
• Homepage:
• Size: 2.93 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Practicum 2 - Numerical Computation

    Name           : Rafi Aliefian Putra Ramadhani        

    NRP            : 5025211234

    Kelompok       : C11 (Alya Putri Salma, Kartika Diva Asmara Gita)

## Source Code with Python (Py)

```R

import numpy as np

import math 

def f(x):

    return math.sin(x)

def CompTrapzRule (points: np.ndarray) -> float:

    h = points[1] - points[0]

    if(points.size < 2): 

        return -1

    else:

        temp = 0

        for i in range(1, points.size - 1):

            temp += f(points[i])

        return h / 2 * (f(points[0]) + 2 * temp + f(points[points.size - 1]))

def romberg(a, b, iterasi):

    matrix = [] #untuk menyimpan nilai romberg

    for _ in range(0, iterasi): 

        matrix.append([None for _ in range(0, iterasi)])

    

    section = 1 #jumlah untuk Composite Trapezoid Rule

    iteration = 0 #awal iterasi dari perulangan while

    while (section < 2**iterasi):

        points = np.linspace(a, b, section + 1) #untuk mendapatkan poin tersebar merata

        matrix[iteration][0] = CompTrapzRule (points) 

        section *= 2

        iteration += 1

    

    #menghitung integrasi romberg

    for i in range(1, iterasi):

        for j in range(1, iterasi):

            if (i < j):

                continue

            

            #rumus romberg

            temp = (4*(j) * matrix[i][j - 1] - matrix[i - 1][j - 1]) / (4*(j) - 1)

            matrix[i][j] = temp

    return matrix[iterasi - 1][iterasi - 1]

    

def main():

    a = 0  #batas bawah    

    b = math.pi #batas atas

    iterasi = 9    

    hasil = romberg(a, b, iterasi)

    print("Romberg ({},{}) = {}".format(iterasi, iterasi, hasil))

if __name__ == "__main__":

    main()

```

## Output Program :

![pr2](https://user-images.githubusercontent.com/91828276/206484653-35674f18-4a84-427e-8807-96b724051b9a.png)

## Thank you Numerical Computation !!