The explicit solution of the equation of heat conduction

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Abstract
In this paper we examine the n-dimensional extensions of the finite-difference schemes proposed by (a) Larkin, Lees, and Saul'yev and (b) du Fort and Frankel for the solution of the differential equation ut = uxx. The formulae obtained are explicit and stable for all values of the mesh ratios, but these ratios are found to be limited in practice by truncation error considerations. A comparison of the storage requirements and computing efficiency is made with other well known methods.

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