Numerical-Methods

I took a course in numerical methods. This repository is the result of me coding everything I learned in that course.

Interpolation

Given a set of points and the corresponding function values, can we estimate the original function?

I have implemented the following methods:

• Lagrange Polynomials
• Natural Cubic Spline

Numerical Integration

Given a set of points and the corresponding function values, can we estimate the integral of the original function?

I have implemented the following methods:

• Lagrange Interpolation + Integration
• Compound Quadrature
  • Newton-Cotes (equally spaced subintervals)
    • Simpson's Rule (m=3)
    • Trapezoidal Rule (m=2)
• Guassian Quadrature

Solving Linear System of Equations

Given a system of linear equations, find the solution.

I have implemented the following methods:

• LU Decomposition
• LUP Decomposition
• Least Squares Method

Solving Nonlinear System of Equations

Given any system of equations, find a solution.

I have implemented the following methods:

• Bisection Method
• Secant Method
• Newton's Method
• Generalized Newton's Method (for system of vector equations)

Relaxation Methods for Solving Systems of Equations

Given a system of equations, find a solution efficiently to a given tolerance.

I have implemented the following methods:

• Point-Jacobean
• Guass-Seidel
• Successive Over Relaxation

Optimization

Given an objective function and set of constraints, find the minimizer.

I have implemented the following methods:

• Golden Section Search

Taylor Table

Given a derivative estimator, find its associated error

ODE Solvers

Given an ODE, solve it numerically using time marching.

I have implemented the following time marching methods:

• Explicit Euler
• Implicit Euler
• Leapfrog
• McCormmack
• RK4

Note: It is very easy to add additional methods