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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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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


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:
  • MathSciNet review: 0413523