Models Methods Software

Dan Hughes

Lack of Convergence, Under-Resolution, and Numerical Errors

The Basic Hypotheses

The following is well known but because it is the focus of this discussion I list it for handy reference.

Convergence is Paramount; Nothing else Counts

The fundamental objective of numerical solution of systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs) is to ensure that the approximations made in order to solve the equations do not in fact influence the solutions. In the case of systems of algebraic equations, it must be shown that the stopping criteria applied to iterative solution methods does not influence the accepted solutions. The solutions are independent, to an acceptable level, of the stopping criteria, and the calculated numbers satisfy the equations.
Continue reading

February 13, 2007 Posted by | Calculation Verification, Verification | , , , | 6 Comments