Existence of Gauss interpolation formulas for the one-dimensional heat equation

Author:
David L. Barrow

Journal:
Math. Comp. **30** (1976), 24-34

MSC:
Primary 65M05

DOI:
https://doi.org/10.1090/S0025-5718-1976-0413523-0

MathSciNet review:
0413523

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Abstract: Let be a Jordan arc in the *x-t* plane satisfying , and when . Let . We prove the existence of Gauss interpolation formulas for *C* and the point , for solutions *u* of the one-dimensional heat equation, . Such formulas approximate 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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DOI:
https://doi.org/10.1090/S0025-5718-1976-0413523-0

Article copyright:
© Copyright 1976
American Mathematical Society