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Polynomial approximations to the solution of the heat equation

Published online by Cambridge University Press:  24 October 2008

R. E. Scraton
R. E. Scraton
Affiliation:
University of Bradford
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Abstract

An approximation is found to the solution of the partial differential equation

in the region −1 ≤ x ≤ 1, t > 0, where u satisfies a general linear boundary condition on x = ± 1. This approximation is a polynomial in x, and is an exact solution of a perturbed form of the differential equation. By choosing the perturbation appropriately, this approach is mathematically equivalent to some recent methods for solving the differential equation in the form of a Chebyshev series. Better approximations to the required solution (and particularly to the eigenvalues) are obtained by choosing the perturbation to satisfy a least squares criterion.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 73 , Issue 1 , January 1973 , pp. 157 - 165
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

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