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The G-functions Series Method Adapted to the Numerical Integration of Parabolic PDE

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Document pages: 13 pages

Abstract: The Method Of Lines (MOL) and Scheifele’s G-functions in the design ofalgorithms adapted for the numeric integration of parabolic PartialDifferential Equations (PDE) in one space dimension are applied. Thesemi-discrete system of ordinary differential equations in the time direction,obtained by applying the MOL to PDE, is solved with the use of a method of AdaptedSeries, based on Scheifele’s G-functions. This methodintegrates exactly unperturbed linear systems of ordinary differential equations,with only one G-function. An implementationof this algorithm is used to approximate the solution of two test problemsproposed by various authors. The results obtained by the Dufort-Frankel, Crank-Nicholsonand the methods of Adapted Series versus the analytical solution, show theresults of mistakes made.

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