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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Existence of Gauss interpolation formulas for the one-dimensional heat equation
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by David L. Barrow PDF
Math. Comp. 30 (1976), 24-34 Request permission

Abstract:

Let $C = \{ (x(s),t(s)):a \leqslant s \leqslant b\}$ be a Jordan arc in the x-t plane satisfying $(x(a),t(a)) = (a,{t_ \ast }),(x(b),t(b)) = (b,{t_\ast })$, and $t(s) < {t_\ast }$ when $a < s < b$. Let $a < {x_\ast } < b$. We prove the existence of Gauss interpolation formulas for C and the point $({x_\ast },{t_\ast })$, for solutions u of the one-dimensional heat equation, ${u_t} = {u_{xx}}$. Such formulas approximate $u({x_\ast },{t_\ast })$ in terms of a linear combination of its values on C. The formulas are characterized by the requirement that they are exact for as many basis functions (the heat polynomials) as possible.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 24-34
  • MSC: Primary 65M05
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0413523-0
  • MathSciNet review: 0413523