Lecture 10 of Numerical methods for differential equations (CTB2400)

• The following subjects are discussed:
  
  
  • Neumann boundary condition, general boundary value problem
  • convection-diffusion equation, upwind discretisation
  • non-linear equation, rounding errors
  • Bisection method, convergence, termination criterion
  • Fixed point iteration, linear convergence
    
    
  Corresponding pages in the book: pages 103-114 except section 7.5 and 7.7. The lecture is also available via collegerama (first hour), collegerama (contains the material of the second hour, you can start from the 25th minute of the video).
  
  
• Historical remarks
  
  
• Easy exercises of Chapter 4.
  
  
• Exercises 2 and 4 of page 116 can be made ( answers)
  
  
• Additional information
  
  
  • Illustration of a convergent fixed point process.
  • Illustration of a divergent fixed point process.