Can I Trust This Software Package? An Exercise In Validation Of Computational Results

Authors

  • Mordechai Shacham Ben-Gurion University of the Negev
  • Neima Brauner Tel-Aviv University
  • W. Robert Ashurst Auburn University
  • Michael B. Cutlip University of Connecticut

Abstract

Mathematical software packages such as Polymath, MATLAB, and Mathcad are currently widely used for engineering problem solving. Applications of several of these packages to typical chemical engineering problems have been demonstrated by Cutlip, et al.[1] The main characteristic of these packages is that they provide a “problem-solving environment (PSE)” (Enright[2]) rather than just scientific subroutine libraries callable from programming languages that were popular a few years ago. For routine use of the software packages for problem solving, there is no need to be an expert in either numerical methods or programming. In most cases it is sufficient to specify the mathematical model of the problem using the syntax required by the package. The technical details of the solution are carried out by the package. However, there are cases where the solution is obviously incorrect and/or the program stops with an error message. The failure of a software package to reach a correct solution is commonly due to the presence of errors in the mathematical model or because of the selection of an inappropriate solution algorithm and/or inappropriate algorithm parameters (such as initial estimates, error tolerances, etc). Validation of the mathematical models has been discussed in detail by Brauner, et al.[3] In this paper we present an exercise that can be used to educate students to identify difficulties associated with an algorithm used for the solution of a problem and to select appropriate parameters for the algorithm. This exercise involves numerical solution of a system of ordinary differential equations (ODEs). It can be used at two levels. 1. The first is in courses where students routinely use numerical software for solving ODEs (i.e., Reaction Engineering, Process Control, and Process Simulation). In such courses, this part of the exercise can be used to demonstrate that computer solutions can be inaccurate or even completely incorrect, and that it is always necessary to validate a numerical solution. 2. At the more advanced level, the second part of the exercise can be used in courses related to mathematical modeling and numerical analysis. In such courses this part of the exercise provides training and demonstration of advanced topics, such as error estimation and step size control, error propagation and stiffness of ODEs.

Author Biographies

Mordechai Shacham, Ben-Gurion University of the Negev

Mordechai Shacham is the Benjamin H. Swig professor of chemical processes and former chair at Ben-Gurion University of the Negev in Israel. He received his B.Sc. and D.Sc. degrees from the Technion, Israel Institute of Technology. His research interests include analysis, modeling and regression of data, applied numerical methods and prediction, and consistency analysis of physical properties. He is past president and an honorary fellow of the Israel Institute of Chemical Engineers, and the recipient of the 2000 CACHE Award for excellence in computing in chemical engineering education.

Neima Brauner, Tel-Aviv University

Neima Brauner is a professor at Tel-Aviv University in Tel Aviv, Israel. She received her B.Sc. and M.Sc. in chemical engineering from the Technion Institute of Technology in Haifa, Israel, and her Ph.D. in mechanical engineering from the Tel-Aviv University. Her research interests include hydrodynamics and transport phenomena in two-phase flow systems and development of interactive statistical and numerical methods for data analysis in process analysis and design. She is an editor for Reviews in Chemical Engineering, and associate editor of Heat Transfer Engineering.

W. Robert Ashurst, Auburn University

W. Robert Ashurst is currently an assistant professor of chemical engineering at Auburn University. His research focuses on design of molecular precursors for advanced mono/ayer films, tribology at the micro- and nano-scale, and the influence of surface chemical treatments on micro- and nano-scale devices. He completed his Ph.D. in chemical engineering at the University of California at Berkeley in 2003 under the support of a National Science Foundation Graduate Fellowship. He is an active member of A!ChE.

Michael B. Cutlip, University of Connecticut

Michael B. Cutlip has spent his entire academic career at the University of Connecticut, where he served as department head of chemical engineering and director of the university's honors program. He is a former chair and national program chair for the Chemical Engineering Division, and he co-chaired the ASEE Summer School for chemical engineering faculty in 2002. He is also co-author of the POLYMATH software package.

Downloads

Published

2008-01-01

Issue

Vol. 42 No. 1 (2008): Winter 2008

Section

Class and Home Problems