Project for Numerical Analysis/matlab Program

Project for Numerical Analysis/matlab Program

Problem 1: Linear System

(1)    Program M-files for solving both upper triangular system by back-substitution and lower triangular system by forward substitution;
(2)    Program an M-file for LU decomposition with partial pivots.
(3)     .

Problem 2: Non-Linear Equations

(1)    Program M-files for bisection method, Newton’s method and Secant method for finding roots of equations
(2)    Applying the above programs for the equation for 8 steps of iteration, with the numbers in Format Long.

Problem 3: Numerical Integration

(1)    Program M-files for the composite mid-point rule, composite trapezoid rule and composite Simpson’s rule;
(2)    Applying the above to compute  with  ,

Problem 4: ODE-IVP

(1)    Program M-files for Euler method and Runge-Kutta method for solving ODE.
(2)    Applying the above for   on the interval  with