numeth-Numerical-Methods-Library

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numeth-Numerical-Methods-Library

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A fully functional Python package implementing core numerical methods for engineering and applied mathematics. Designed for usability and educational clarity.

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# numeth

A fully functional Python package implementing core numerical methods for engineering and applied mathematics. Designed for usability and educational clarity.

## Installation

Install via pip:

```
pip install numeth
```

## Quick Start

Here's a simple example using the Newton-Raphson method to find the square root of 2:

```python
from numeth import newton_raphson

def f(x):
    return x**2 - 2

def df(x):
    return 2 * x

root, iterations, converged = newton_raphson(f, df, x0=1.0, tol=1e-6, max_iter=100)
print(f"Root: {root}, Iterations: {iterations}, Converged: {converged}")
# Output: Root: 1.414213562373095, Iterations: 4, Converged: True
```

## Visualization

You can easily visualize the convergence or the results of any numerical method using the `.graph()` method.

```python
import numeth

# Integration visualization
tr = numeth.trapezoidal(lambda x: x**2, 0, 1)
tr.graph()

# Root finding visualization
sol = numeth.bisection(lambda x: x**2 - 2, 0, 2)
sol.graph()
```

The `.graph()` method provides a visual representation of how the algorithm works, including function plots, integration areas, root markers, and tangent lines for differentiation.

### Supported Methods for Visualization
Visualization is currently supported for almost all modules:
- **Integration**: All methods supported.
- **Root Finding**: All methods supported.
- **Differentiation**: All methods supported.
- **Interpolation**: All methods supported.
- **Optimization**: All methods supported.

*Note: Linear Algebra methods (Gauss Elimination, LU Decomposition, Jacobi, Gauss-Seidel) currently do not support `.graph()` because they operate on vectors/matrices rather than single-variable functions.*

## Supported Methods

### Integration
- Trapezoidal Rule (single and composite)
- Simpson’s 1/3 Rule (single and composite)
- Simpson’s 3/8 Rule
- Gaussian Quadrature (2-point and 3-point)

### Differentiation
- Forward difference (first derivative)
- Backward difference (first derivative)
- Central difference (first derivative)
- Central difference (second derivative)
- Richardson extrapolation (first derivative)

### Root Finding
- Bisection Method
- Newton-Raphson Method
- Secant Method
- False Position Method

### Interpolation
- Linear Interpolation
- Lagrange Interpolation
- Newton’s Divided Difference Interpolation

### Linear Algebra
- Gauss Elimination with partial pivoting
- LU Decomposition (Doolittle’s method)
- Jacobi Iterative Method
- Gauss-Seidel Iterative Method

### Optimization
- Golden Section Search (minimization)
- Newton’s Method for Optimization (1D)

## How to Contribute or Report Issues

Contributions are welcome! Please submit pull requests or open issues on the [GitHub repository](https://github.com/AbhisumatK/numeth-Numerical-Methods-Library).

## License

This project is licensed under the MIT License - see the [LICENSE](https://github.com/AbhisumatK/numeth-Numerical-Methods-Library/blob/main/LICENSE) file for details.

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