mth308lib

A Python library implementing core numerical methods for MTH308, including root-finding, linear systems, interpolation, and ODE solvers.

Features

• Root Finding:

  • Bisection method
  • Regula Falsi
  • Modified Regula Falsi
  • Newton-Raphson
  • Secant method

• Linear Systems:

  • Gaussian Elimination
  • Gauss-Seidel
  • Jacobi
  • SOR (Successive Over-Relaxation)
  • LU Decomposition (Doolittle & Crout)
  • Power Method (dominant eigenvalue/vector)

• Interpolation:

  • Divided Difference Table
  • Newton Divided Difference

• Numerical Integration:

  • Trapezoidal Rule
  • Simpson's 1/3 Rule

• ODE Solvers:

  • Euler's Method
  • Runge-Kutta 4th Order (RK4)

Installation

From the root directory, run:

pip install .

Usage

Import any function directly from the package:

from mth308 import (
    bisection_method, regula_falsi, modified_regula_falsi, newton_raphson, secant_method,
    gaussian_elimination, gauss_seidel, jacobi, sor_solver, lu_doolittle, lu_crout, power_method,
    divided_difference_table, newton_divided_diff,
    trapezoidal_rule, simpsons_one_third,
    euler_method, rk4
)

# Example: Find root of x^2 - 2 = 0 using bisection
root, iterations, converged = bisection_method(lambda x: x**2 - 2, 0, 2)
print("Root:", root)

Testing

Run all tests with:

python -m unittest discover tests

File Structure

mth308lib/
│
├── mth308/
│   ├── __init__.py
│   ├── bisection.py
│   ├── ctr_num_int.py
│   ├── divided_diff.py
│   ├── euler.py
│   ├── gauss_seidel.py
│   ├── gaussian_elim.py
│   ├── jacobi.py
│   ├── lu.py
│   ├── mrf.py
│   ├── newton_raphson.py
│   ├── power_method.py
│   ├── regula_falsi.py
│   ├── rk4.py
│   ├── secant.py
│   ├── simpsons.py
│   └── sor.py
│
├── tests/
│   └── test_all.py
│
├── setup.py
└── README.md

License

IITK