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Improved finite-difference solutions of the diffusion equation for heat conduction

✍ Scribed by Bhattacharya, M. C.

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
387 KB
Volume
9
Category
Article
ISSN
1069-8299

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✦ Synopsis

A number of improved finite-difference solutions of explicit form have been reported recently. The choice of a particular solution of these improved explicit forms is dependent on the value of the non-dimensional time step as well as whether the process involves cooling or heating. The conditions for stable operation are clarified in the paper. Two new improved solutions of implicit forms are also reported in the paper. These new solutions give better accuracy compared to the conventional Crank-Nicolson and pure implicit methods, and have unrestricted stability.

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In this article, we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two-dimensional heat equation. We employ, respectively, second-order and fourth-order schemes for the spatial derivatives, and the discr