A finite difference formula of explicit type for pure Initial Value Problem of Heat Equation

Dhruti B Joshi, A K Desai


In this paper we derive an iterative finite difference formula of explicit type to solve pure initial value problem of heat equation. To explain the development of improved finite difference formula for a given parabolic partial differential equation the simple dimensionless heat equation is used. In unbounded domains implicit methods are not applicable as they generate infinite matrices. Thus it is necessary to find more improved equations of explicit type. We apply finite difference formulas in a specific way and obtain a new formula where the truncation error gets reduced. Also the convergence limit and therefore stability gets improved.

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William F. Ames, Numerical Methods For Partial Differential equations, Academic Press,

New York, San Francisco, 1977.

Bernstein, D. L. Existance Theorems In Partial Differential Equtions. Princeton University

Press, N. J. 1950.

Friedman, Partial Differential equations of Parabolic Type. Prentice - Hall Inc., Englewood

Cliffs, N. J. 1964.

G. D. Smith, Numerical Solutions of Partial Differential Equations, Ames House, London,

Oxford University Press, New York, Toronto,1965.

Ian Sneddon, Elements Of Partial Differential Equations, Dover Publications, 2006.


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