CS-381: Engineering Systems Analysis Using Numerical Methods

Fall 1998

Homework Assignments

Homework 1: Error analysis; Analyse and design systems represented by a nonlinear equation.
- Specifications:
  - Calculate absolute error of a real solution of a standard quadratic equation given absolute error of the coefficients.
  - Calculate three iterations using bisection, Newton-Raphson, Secant, and fixed-point iteration for a system represented by the following equation x³+3x²-6x-8 = 0.
Homework 2: Analyse and design systems represented by a system of equations.
- Specifications:
  - Solve the system of problem 41 of page 97 in text for three iterations.
  - Solve the system of problem 6 of page 201 in text by Gauss-Jacobi and Gauss-Seidel methods beginning with approximate solution (2,2,-1) for three iteration steps.
  - What are the values of the default initial approximate solution in the above problem.
  - Solve the system of problem 55 of page 205 in text by relaxation method beginning with default initial approximate solution for three iteration steps.
Homework 3: Error Analysis;Polynomial Interpolation
- Specifications:
  - Lagrange: Problem 1 page 300 for x=2.5
  - Error Analysis: Problem 4 page 300. Use the equation.
  - Divided Difference: Repeat problem 1
  - Neville: Problem 6 page 300
Homework 4: Spline
- Specifications:
  - Cubic Spline: Problem 34 & 35 page 302
  - Bezier Spline: Problem 43
Homework 5: Ordinary Differential Equations
- Specifications:
  - Euler Method: Problem 6 page 456
  - Runge-Kutta Method: Problem 12 page 456
Homework 6: Ordinary Differential Equations(cont)
- Specifications:
  - n-order systems: Problems 47 and 54 page 459
  - Adams-Moulton Method:For the first order, initial value problem given in hand-out and discussed in class (dy/dx=1-x+4y; y(0) = 1), use the initial value and values at y(0.1),y(0.2), y(0.3) derived using RK4 method to calculate the value at y(0.4) using Adams-Moulton method.