On the Solution of the Diffusion Equations by Numerical Methods

[+] Author and Article Information
H. Z. Barakat

Department of Mechanical Engineering, University of Michigan, Ann Arbor, Mich.

J. A. Clark

Heat Transfer Laboratory, Department of Mechanical Engineering, University of Michigan, Ann Arbor, Mich.

J. Heat Transfer 88(4), 421-427 (Nov 01, 1966) (7 pages) doi:10.1115/1.3691590 History: Received June 25, 1964; Revised January 14, 1965


An explicit-finite difference approximation procedure which is unconditionally stable for the solution of the general multidimensional, nonhomogeneous diffusion equation is presented. This method possesses the advantages of the implicit methods, i.e., no severe limitation on the size of the time increment. Also it has the simplicity of the explicit methods and employs the same “marching” type technique of solution. Results obtained by this method for several different problems are compared with the exact solution and with those obtained by other finite-difference methods. For the examples solved the numerical results obtained by the present method are in closer agreement with the exact solution than are those obtained by the other methods.

Copyright © 1966 by ASME
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