Approximate Solution of Heat Equation with Chebyshev Heat Polynomial

IR

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  • 熱多項式を用いた境界法による熱方程式の解
  • ネツ タコウシキ オ モチイタ キョウカイホウ ニヨル ネツ ホウテイシキ ノ カイ

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Heat polynomials have been applied to study the analytic solution of the initial value problem of the heat equation. Since the polynomials satisfy the heat equation the approximate solution of the initial value problem by using the polynomials become an interpolation problem. Therefore the approximate solution is determined from the given initial data since the solution method involves no integration and no discretization with respect to the time-space domain. In order to apply the approach to an initial-boundary value problem, we present an approximation method with Chebyshev heat polynomials which are proposed in this paper. A recurrence formula to generate Chebyshev heat polynomials is presented. Moreover we show that the present method give accurate approximate solutions by numerical experiments.

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