📘 Numerical Methods (MATLAB + Python)

This repository contains MATLAB and Python implementations of fundamental numerical methods, including curve fitting, numerical integration, interpolation, solving linear systems, differential equations, and root-finding.

📖 Implemented Methods

🔹 Curve Fitting

• Linear Regression
• Least-Squares Polynomials

🔹 Numerical Integration

• Composite Boole Method
• Composite Simpson 1/3 Method
• Composite Simpson 3/8 Method
• Composite Trapezoidal Method
• Composite Weddle’s Rule
• Unequally Spaced Trapezoidal Rule
• Gauss–Legendre Quadrature

🔹 Interpolation

• Lagrange Method
• Newton Method

🔹 Linear System of Equations

• Direct methods: Backward/Forward Substitution, Cholesky, Crout, Doolittle, Gaussian Elimination, Gauss–Jordan
• Iterative methods: Jacobi, Gauss–Seidel

🔹 Ordinary Differential Equations (IVPs)

• Euler’s Method
• Midpoint Method
• Taylor Methods (Order 2 & 4)
• Runge–Kutta Methods (RK2, RK3, RK4)

🔹 Root-Finding (f(x) = 0)

• Bisection Method
• False-Position Method
• Fixed-Point Iteration
• Newton–Raphson Method
• Secant Method