Numerical Methods Console App

This is the repository for a C++ console application to implement and solve various mathematical problems with the use of numerical methods. This repository houses functions related to root-finding in non-linear equations, solving systems of linear equations, differential equations, and matrix operations.

Features :

i) Root Finding Algorithms

1. Bisection Method : Root finding by the method of interval bisection.
2. False Position Method : A root finding scheme using linear interpolation.
3. Secant Method : Approximates position of roots using secant lines.
4. Newton-Raphson Method : A root-finding algorithm using derivatives.

ii) Linear Equation Solvers

1. Jacobi Iteration : solves linear systems iteratively.
2. Gauss-Seidel Method : Like Jacobi, but immediate updates
3. Gaussian Elimination : Stores a matrix in row echelon form.
4. Gauss-Jordan Elimination : solves systems by converting to reduced row echelon form.
5. LU Factorization : decomposes a matrix into lower and upper matrices.

iii) Differential Equation Solvers

1. Runge-Kutta Method : solves first-order differential equations with greater accuracy.

iv)Matrix Operations

1. Matrix Inversion : Computes the inverse of a matrix if it exists.