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https://doi.org/10.1016/S0893-9659(00)00055-0

has been cited by the following article:

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

  AUTHORS: Mónica Cortés-Molina, José Antonio Reyes, Fernando García-Alonso

  KEYWORDS: Series Method, Numerical Solutions, Parabolic Initial-Boundary Value Problems, Method of Lines

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.6 No.1, January 18, 2018

  ABSTRACT: The Method Of Lines (MOL) and Scheifele’s G-functions in the design of algorithms adapted for the numeric integration of parabolic Partial Differential Equations (PDE) in one space dimension are applied. The semi-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 Adapted Series, based on Scheifele’s G-functions. This method integrates exactly unperturbed linear systems of ordinary differential equations, with only one G-function. An implementation of this algorithm is used to approximate the solution of two test problems proposed by various authors. The results obtained by the Dufort-Frankel, Crank-Nicholson and the methods of Adapted Series versus the analytical solution, show the results of mistakes made.