Lecture 12 of Numerical methods for differential equations (CTB2400)

• The following subjects are discussed:
  
  
  • Fixed point iteration, linear convergence
  • non-linear equation, Newton Raphson, quadratic convergence, termination criterion
  • Newton Raphson for systems of non-linear equations
    
    
  Corresponding pages in the book: pages 44-49 and 114. The lecture is also available via collegerama.
  
  
• Easy exercises of Chapter 4.
  
  
• Historical remarks
  
  
• Exercises 3 and 4 of page 47 can be made ( answers)
  
  
• Additional information
  
  
  • Applications from water problems.
  • Explanation of the Newton Raphson method (Dutch).
  • English explanation of the Newton Raphson method with a nice Java example.