Numerical Methods using MATLAB

Explore MATLAB code for the bisection method, a bracketing technique, detailing how to define the function, apply initial guesses, and achieve the required accuracy.

Learn how to implement the Newton-Raphson method in MATLAB to find roots of equations, including choosing initial guesses, iterating until accuracy criteria are met, and displaying results.

Solve linear simultaneous equations in MATLAB using the Gauss elimination method. Apply backward substitution on the augmented matrix to compute the solution X.

Develop MATLAB code for the Gauss-Seidel method to solve linear systems by iteratively updating x, y, and z. Ensure convergence through diagonal dominance and user-driven inputs.

Learn to implement the Thomas algorithm in MATLAB to solve tri-diagonal systems via forward elimination and backward substitution, including building the A and B inputs and displaying the solution X.

Learn how to implement Euler's method in MATLAB to solve ordinary differential equations, including setup with x0 and y0, step size h, and computing y values at successive x.

Master the Runge-Kutta 4th order method in MATLAB to solve the differential equation dy/dx = x^2 + y^2 with given initial values, step size, and number of steps.

solve a second-order differential equation in matlab by converting to a first-order system, applying runge-kutta, with initial conditions, for simultaneous equations.

Explore solving the Laplace equation with MATLAB by implementing finite difference schemes, building the grid, applying boundary conditions, and writing MATLAB code to compute numerical solutions.

Learn to implement Lagrange's interpolation in MATLAB by building a script that inputs data points, computes the interpolating polynomial via a loop, and outputs the results.

Apply Newton's forward interpolation in MATLAB to compute interpolated values from data, initialize forward differences, and implement a loop to handle input x values and results.