Abstract
<p>Interpolation formulas of the form</p><p> </p><p>u(x_*1 , ... ,x_(* n),t_*) ~= Sum_{i=1}^{N} A_i u(v_i1,...,v_in, t_i)</p><p>are presented. These formulas are based on the heat polynomials of Appell. The point (x_{* 1}, ... x_{* n}t_*) is in the interior of an (n+1) dimensional region, R_n+1, and the points (v_i1,...,v_in, t_i) are on the boundary of R_n+1. These formulas can be used to approximate the solution of the heat conduction problem in R_n+1. The relationship between formulas of the above type of deqree 2 in R_n+1 and the second degree harmonic interpolation formulas of Stroud, Chen, Wang, and Mao in R_n is persented. Some higher degree formulas for special regions in R_2 are also developed.</p>
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