1. Some simple space discretizations and modified equations. 2. Space discretizations: general considerations. 3. Time discretizations: MOL and von Neumann stability. 4. Linear space discretizations and positivity. 5. A nonlinear advection discretization by flux-limiting. 6. Positive time discretizations. 7. Boundary conditions and spatial accuracy. 8. Boundary conditions and temporal accuracy. 9. Time splitting methods.

Department of Numerical Mathematics [NM]
Discretization of evoluation problems

Hundsdorfer, W. (1996). Numerical solution of advection-diffusion-reaction equations : lecture notes for Ph.D. course, 1996, Thomas Stieltjes Institute. Department of Numerical Mathematics [NM]. CWI.