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.