Error Analysis
 

Hello CFD friends

I am working on an error analysis of a time marching scheme.Can anybody help me to find out how to calculate error for every time step and then the for a finite no. of time steps.By the way I am dealing with adams Bashforths time stepping method.

Thank You in advance.

Re: Error Analysis
 

Are you integrating odes or pdes? If they are odes, look up a book on odes, and read the chapter on multi-step and BDF methods. Analysing consistency is easy (and well known for Adams Bashforth) but stability (and types of stability like R-stability, alpha-stabililty) is a little more complicated than one-step methods. The best book I have come across is by E Hairer, SP Norsett and G Wanner, called "Solving ordinary differential equations".

If you are dealing with pdes, there are similar methods of analysis, but often local truncation errors scale as some non-linear product of spatial grid size and the local time step. J. W. Thomas's book called "Numerical Partial Differential Equations: Finite Difference Methods" should give you some good help.

Re: Error Analysis
 

Thank u 'whatever' for the information I will go ahead and find these books