Similarity and Generalized Finite-Difference Solutions of Parabolic Partial Differential Equations

[+] Author and Article Information
A. M. Clausing

Department of Mechanical Engineering, University of Illinois at Urbana-Champaign, Urbana, Ill.

J. Appl. Mech 39(2), 584-590 (Jun 01, 1972) (7 pages) doi:10.1115/1.3422721 History: Received October 09, 1970; Revised March 11, 1971; Online July 12, 2010


Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

Copyright © 1972 by ASME
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