Further reading 


L. Davidson, "Derivations of some Stability Conditions Using von Neumann Analysis"

In this short note Neumann stability analysis is used to show: 

  • that a central differencing scheme is unstable; 
  • that both a second-order derivative and a fourth-order derivative are dissipative; this is true for all the nth-order derivative, where n is even; 
  • that the Crank-Nicolson scheme is stable. 
In the final section, we also show that the Gauss-Seidel solver converges if aP > sum( anb

J. Larsson, "A Note on Numerical Errors" 

This note talks about:

  • basic explanation of the effects different spatial derivatives have on a solution
  • how numerical schemes are designed to a certain order
  • why the discretisation of the viscous term is rarely discussed in the literature
  • why the discretisation of the convective term has a strong effects on the solution
  • that upwinding and explicit addition of an even derivative are equivalent
  • Fourier analysis of the discretisation errors
  • how finite difference schemes can be transfered to finite volume schemes
Homepage, Applied Mechanics