Lecture 2 of 'Scientific Computing' (wi4201)

• The following subjects are discussed:
  
  
  • Classification of partial differential equations
  • Eigenvalues and eigenfunctions for the model problem
  • Integration of discretization and solving of the linear systems
  • Finite difference discretization in 1D and 2D
  • In 1D from finite differences to a matrix vector system
  • Properties of the coefficient matrix
  • The finite difference method in 2D
  • Stencil notation
  • Ordering of the unknowns, lexicographic, red-black
  • Block matrices and the final matrix vector system
    
    
• Material is described in pages 6, and 19 - 27 of the lecture notes. Recommended exercises: 3.12.1 - 3.12.10
  
  
• Typo's
  
  
  • Formula (3.20) (k pi x) should be ((k+1/2) pi x) and k^2 pi^2/4 should be ((k+1/2) pi)^2
  • Formula (3.32) left-hand side u_1,j should be u_0,j
  • Line below Formula (3.32) u_0,j should be u_1,j
  • Formula (3.39) sum should run from I = 1 till N+1
  • Formula (3.40) sum should run from I = 1 till (N+1)^2