Expansions in Terms of Heat Polynomials and Associated Functions

Heat polynomial analogues for equations with higher order time derivatives

“…But the only way this condition is possible is thatᾱ · σ β and γ = β −ᾱ · σ , and for any such σ there is only one corresponding γ . Thus we may rewrite (28) in the equivalent formulation…”

“…As there are only a finite number of powers x γ with γ β, (28) shows that p β,k (x, t) is a polynomial in x when t is held fixed. If the operator L of (11) contains a zero order term-that is, if some nonzero a α appears corresponding to α = (0, .…”

“…These polynomials appear in early work of Appell [1] on the heat equation, and were later investigated in detail by Rosenbloom and Widder [28,[31][32][33]. The polynomials are particularly useful in solving the Cauchy problem…”

Direct and inverse heat transfer in non-contacting face seals

“…In the papers mentioned above, stationary problems or problems brought to be stationary through time discretisation are considered. Rosenbloom and Widder in the paper of [16] obtained Trefftz functions for 1D non-stationary heat conduction equation, in which 'time' occurred as one of the variables. A number of papers have been published in this trend.…”

New type of basic functions of FEM in application to solution of inverse heat conduction problem

“…[4], and their applications t1~3'Sj. Since heat polynomials by identity fulfil the heat conduction equation, its solution may be sought in the form of linear combination of heat polynomials.…”