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https://github.com/nazmusweb-coding/numerical-methods

Some Numerical Methods Implementation in C++ and Python
https://github.com/nazmusweb-coding/numerical-methods

cpp numerical-algorithms numerical-calculations numerical-computation numerical-integration numerical-methods python

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Some Numerical Methods Implementation in C++ and Python

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README 

        
# Numerical Methods Repository



Welcome to the Numerical Methods repository! This project includes implementations of various numerical methods in both C++ and Python. The Python implementations are designed to mimic C++ conventions to help C++ coders transition smoothly to Python.



## Methods Implemented



### 1. Simple Iteration / Brute Force Method

A basic iterative approach for solving equations.



### 2. Newton-Raphson Method

A numerical technique for finding successively better approximations to the roots of a real-valued function.



### 3. Bisection Method

A root-finding method that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing.



### 4. Numerical Differentiation

   - **Forward Finite Differences:** Approximates the derivative of a function using forward differences.

   - **Central Finite Differences:** Approximates the derivative using central differences.

   - **Backward Finite Differences:** Approximates the derivative using backward differences.



### 5. Numerical Integration

   - **Trapezoidal Rule:** Approximates the integral of a function using trapezoids.

   - **Simpson's 1/3 Rule:** Approximates the integral of a function using parabolic segments.

   - **Simpson's 3/8 Rule:** A variation of Simpson's rule using cubic polynomials.

   - **Simpson's 1/3 Double Integration Rule:** Extends Simpson's 1/3 rule to double integrals.



### 6. Interpolation

   - **Linear Interpolation:** Estimates unknown values by assuming a linear relationship between known values.

   - **Lagrange's Interpolation:** Provides a polynomial interpolation through a set of data points.

   - **Newton's Method:** Provides an interpolating polynomial in Newton form.



## Installation



To use the C++ and Python implementations, you'll need to have the appropriate compilers or interpreters installed:



### C++:

- Install a C++ compiler (e.g., `g++` or `clang++`).



### Python:

- Ensure you have Python 3.x installed. You can download it from [python.org](https://www.python.org/).



## Usage



### C++



To compile and run the C++ code, navigate to the C++ source directory and use the following commands:



```bash

g++ -o method_name method_name.cpp

./method_name

```



##### Alternative Approache:

You can use an [online compiler](https://www.programiz.com/cpp-programming/online-compiler/) such as Programiz to compile and run your C++ code directly in the browser.



### Python



To run the Python code, navigate to the Python source directory and use the following command:



```bash

python method_name.py

```



##### Alternative Approaches:

- Google Colab: Use [Google Colab](https://colab.research.google.com/notebooks/intro.ipynb#scrollTo=5Y9LXc69ndOO) to run your Python code in a cloud-based environment.



- JupyterLite: Try [JupyterLite](https://jupyterlite.github.io/demo/lab/index.html) (to try without login) for an online Jupyter notebook experience without needing to log in.



These platforms provide suitable environments for Python and are generally better than other online interpreters available.