Lecture 2 of Numerical methods for differential equations (CTB2400)

• The following subjects are discussed:
  
  
  • First order derivative, approximation error, roundoff error
  • general formula, relation differentiation and interpolation
  • higher order derivative
  • Richardson error estimation and extrapolation
    
    
  Corresponding pages in the book: pages 25-37, without section 3.5 and 3.7.3. The lecture is also available via collegerama.
  
  
• Historical remarks
  
  
• Easy exercises of Chapter 3.
  
  
• Exercises 1, 2, and 4 of page 36 and 37 can be made ( answers)
  
  
• Additional information
  
  
  • Slide showing approximation and roundoff error for numerical differentiation.
  • Slide showing total error for Forward and Central numerical differentiation.
  • English explanation of first order derivative, roundoff error, higher accuracy and Richardson error estimation and extrapolation.