Numerical Analysis II - Assignment

There are 4 problems you need to solve. For each problem you need show how you got the solution , explain the method you use to get the solution, and include a mat lab program to the solution. You will need to know most of the following 1) Method for solving Non-linear Equation - Newton's Method - Quasi - Newton - Broyden's Method - Fixed Point Iteration 2) Interpolation -Polynomial,Trigonometric,chebyshev Interpolation - Fast Fourier Transformation 3)Numerical Integration - Trapezoid Rule / Simpson Rule -Gaussian Quadrature - Adaptive Quadrature 4)Data Fitting Method - Least Squares Method - sin x , cos x - Exponenital Model - Power Model 5) The Non-linear iterative Method - Conjugate Gradient - GMRes - Preconditioning 6) Power,Inverse Power,shifted Inverse Power 7) ODE -Forward/Backward Euler -Crank Nicklson -RUnge - Kutta _multistep 8) PDE -Poisson Equation -Finite Differences Method -Finite Elements Method - Heat Equations