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Non-Iterative Solution of Ordinary and Partial Differential Equations Using Spreadsheets

[+] Author Affiliations
Ahmad Fakheri

Bradley University

Mohammad H. Naraghi

Manhattan College

Paper No. IMECE2006-14480, pp. 105-112; 8 pages
doi:10.1115/IMECE2006-14480
From:
  • ASME 2006 International Mechanical Engineering Congress and Exposition
  • Innovations in Engineering Education: Mechanical Engineering Education, Mechanical Engineering Technology Department Heads
  • Chicago, Illinois, USA, November 5 – 10, 2006
  • Conference Sponsors: Mechanical Engineering Education, Mechanical Engineering Technology Department Heads
  • ISBN: 0-7918-4781-0 | eISBN: 0-7918-3790-4
  • Copyright © 2006 by ASME

abstract

Typically, in a basic course, the equations are derived and the solutions are presented in tabular or chart from. Spreadsheets provide an attractive option, as most students have access to and are familiar with their use. In this paper, a classic algorithm, called Thomas algorithm, used for the solution of set of algebraic equations whose coefficient matrix is tri-diagonal, is adopted to spreadsheets. It is used to obtain solutions to a number of classical problems in fluid mechanics and heat transfer non-iteratively, and in some cases where the governing equations are non-linear via some iterations. Without needing much programming skills, or needing to learn specialized software, undergraduate students can use this approach and easily obtain the solution to many otherwise difficult problems and study the impact of different parameters.

Copyright © 2006 by ASME

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