Numerical-Analysis

This is a Numerical Analysis course project, implementing numerical analysis methods.

Question 1 - Gaussian Elimination:

This code implements the Gaussian Elimination method to solve a system of linear equations. The user is prompted to enter the number of variables and their corresponding equations. The code then processes the equations and variables and performs Gaussian Elimination to find the solutions for each variable.

Question 2 - Bisection Method:

This code uses the Bisection Method to find the root of a given equation within a specified range. The user needs to provide a function, initial range, and tolerance. The code then iteratively applies the Bisection Method until it finds the root within the specified tolerance.

Question 3 - Unknown Function:

This code defines a function that uses the Bisection Method to find the roots of a given equation within a specified range. The function iteratively applies the Bisection Method until it finds the root(s) within a specific tolerance.

Question 4 - Root Locating:

This code finds the roots of a given function within a specified range using a numerical approach. It divides the range into small segments, checks for sign changes, and applies the Bisection Method to find the roots within each segment.

Question 5 - Newton Method:

This code uses the Newton Method to find the roots of a given equation. It starts with an initial guess and iteratively refines the guess until it finds a root within a specified number of steps.

Question 6 - Power Method and Inverse Power Method:

This code implements the Power Method and Inverse Power Method to find the largest and smallest eigenvalues of a given matrix, respectively.

Question 7 - Simpson, Differential, Integral:

This code calculates the integral and derivatives of a given function using Simpson's rule and central difference methods.

Question 8 - Euler Method with State Space:

This code uses the Euler method to simulate a dynamic system described by a set of first-order differential equations. It iteratively updates the state variables based on the derivatives to model the system's behavior over time.

Question 9 - RK4 for Second Derivation ODE:

This code uses the Runge-Kutta 4th-order method to solve a second-order ordinary differential equation (ODE). It calculates the derivative at different time steps to approximate the solution of the ODE.

Question 10 - Laplace Equation Solving:

This code solves the Laplace equation in a two-dimensional region using the finite difference method. It sets boundary conditions and computes the values for each grid point using the surrounding values until it reaches convergence. The resulting 3D plot visualizes the solution.