Investigating the G-Functions Series Method Adapted to the Numerical Integration of Parabolic PDE | Chapter 6 | Theory and Practice of Mathematics and Computer Science Vol. 5

 In the design of algorithms adapted for the numerical integration of parabolic Partial Differential Equations (PDE) in one space dimension, the Method Of Lines (MOL) and Scheifele's G- functions are applied. The semi-discrete system of ordinary time-direction di fferential  equations obtained by applying MOL to PDE is resolved using an adapted series method based on Scheifele's G-functions. This approach combines precisely undisturbed linear systems with only one G- function of ordinary di erential equations. To approximate the solution of two test problems proposed by separate authors, an implementation of this algorithm is used. Compared to the analytical solution, the results obtained by the Dufort-Frankel, Crank-Nicholson and Adapted Series methods indicate the results of errors made.

Author(s) Details

M. Cort´es-Molina
Dept. of Applied Mathematics, Escuela Polit´ecnica Superior, University of Alicante, Spain.

J. A. Reyes
Dept. of Applied Mathematics, Escuela Polit´ecnica Superior, University of Alicante, Spain.

F. Garc´ıa-Alonso
Dept. of Applied Mathematics, Escuela Polit´ecnica Superior, University of Alicante, Spain.

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