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rvndr November 16, 2003 02:42

Truncation & Discretization error

What is the difference between Truncation error and Discretization error ? Below I have the text book definitions. If i am not wrong both are seems to be same. Is n't it ? Is there any error which is due to boundary conditions mishandling ?

Discretization Error:Is the difference between the exact analytical solution of the partial differential equation and the exact (round-off-free) solution of the corresponding difference equation.

Truncation Error:Is the difference between partial derivative and its finite difference representation.

regards rvndr

Saverio November 17, 2003 00:19

Re: Truncation & Discretization error
Given your definitions above, I believe truncation error concerns itself solely with the choice of difference scheme (say, forward difference), so that without mentioning anything about the PDE itself, we have an error from (df/dx)(i) "=" (f(i+h)-f(i))/h of order O(h).

Discritization error, on the other hand, is more concerned with the entire numerical scheme built to solve your equation(s). Here, issues like stability and convergence are paramount, and the error will be a measure of the validity of the entire scheme. Issues such as time-evolution methods and satisfaction of CFL conditions etc. will enter into measurements of this type of error.

salem November 17, 2003 05:59

Re: Truncation & Discretization error
Hi rvndr

truncation error is the difference between the exact value of the partial derivative and its finite difference representation.

discretization error is the error in the solution to the pde caused by replacing the contiuous problem by a discrete one = difference between the exact ( analytical ) solution of the pde and exact solution of the FDE. salem

alex November 18, 2003 19:36

Re: Truncation & Discretization error
same things pretty much:)

steve podleski November 27, 2003 12:24

Re: Truncation & Discretization error
Another major source of discretization error is grid density.

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