Finite difference methods for diffusion processes

Contents:

• Finite difference methods for diffusion processes
• The 1D diffusion equation
  • The initial-boundary value problem for 1D diffusion
  • Forward Euler scheme
  • Backward Euler Scheme
  • Sparse matrix implementation
  • The \(\theta\) rule
  • The Laplace and Poisson equation
  • Extensions
• Analysis of schemes for the diffusion equation
  • Properties of the solution
  • Analysis of discrete equations
  • Analysis of the finite difference schemes
  • Analysis of the Forward Euler scheme
  • Analysis of the Backward Euler scheme
  • Analysis of the Crank-Nicolson scheme
  • Summary of accuracy of amplification factors
  • Exercise 1: Use an analytical solution to formulate a 1D test
  • Exercise 2: Use an analytical solution to formulate a 2D test

Indices and tables

• Index
• Module Index
• Search Page