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On the numerical integration of the heat equation. (English) Zbl 0211.19202


MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
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References:

[1] Riesz, Nagy: Leçons d’analyse fonctionnelle. Académie des sciences de Hongrie 1952. · Zbl 0046.33103
[2] Descloux: Solution of the heat problem by the method of moments. Report. Department of Mathematics. EPF-Lausanne, 1969
[3] Henrici: Discrete variable methods in ordinary differential equation. John Wiley 1962. · Zbl 0112.34901
[4] Goël: Construction of basic functions for numerical utilisation of Ritz method. Numerische Mathematik12, 435–447 (1968). · Zbl 0271.65061 · doi:10.1007/BF02161367
[5] Lions: Equations différentielles opérationnelles. Berlin-Göttingen-Heidelberg: Springer 1961.
[6] Gear: The automatic integration of stiff ordinary differential equations. IFIP congress 68, Edinburgh.
[7] Descloux: The solution of the heat problem by the method of moments, Part 1. Technical report 12. Computer Center. University of California 12, Berkeley, 1967
[8] Weinberger, A. F.: Variational methods for eigenvalue problems. University of Minnesota, Department of Mathematics. · Zbl 0296.49033
[9] Wilson, Nickel: Application of the finite element method to heat conduction analysis. Nuclear Engineering and Design4, 276–286 (1966). · doi:10.1016/0029-5493(66)90051-3
[10] Descloux: On the heat equation. Math. Z.113, 376–382 (1970). · Zbl 0184.13303 · doi:10.1007/BF01110507
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