Numerical Methods

The following repository consists of various solvers which are helpful in solving systems of equations, optimization and solving ODE using numerical methods

• Gauss-Elimination.cpp is a C++ implementation of Gaussian Elimination for solving a system of linear equations. The program allows 2 ways to compute Forward Elimination. One is through 3 nested for loops for updating values of matrix. The second implementation uses outer product calculation for updating values. The program is made for matrix A of size n*n with entries as a(ij) = max(i,j) and the vector b is a unit vector of length n. The program is tested for multiple values of n and the results are written in a file.
• non_linear_root.py consists of solvers like Bisection method, RegulaFalsi Method and Newton Raphson method etc. to solve a non-linear algebraic equation.
• Numerical_Method_ODE.py consists of solvers like Runge-Kutta method, Midpoint Method, Huen Method, Euler Method to solve an ODE equation.
• Newton_Raphson_system.cpp is a C++ implementation for solving a system of Non-Linear Equation. One has to write Jacobian themselves in this program and recompile and run for other system of non-linear equation.
• RK-4-ODE system.py is an ODE system solver which uses order 4 Runge-Kutta Method. The program is only made for equation of the form : d(y1)/d(x) = f1(x,y1,y2) and d(y2)/d(x) = f2(x,y1,y2)
• cubic_equation_solver as the name suggests solves cubic equation to find its roots. It only works if the polynomial doesn't have complex roots. It uses François Viète formula to compute roots using trignometric functions.