The G-functions Series Method Adapted to the Numerical Integration of Parabolic PDE
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Título: | The G-functions Series Method Adapted to the Numerical Integration of Parabolic PDE |
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Autor/es: | Cortés-Molina, Mónica | Reyes, José Antonio | García-Alonso, Fernando |
Grupo/s de investigación o GITE: | Modelización Matemática de Sistemas |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Matemática Aplicada |
Palabras clave: | Series Method | Numerical Solutions | Parabolic Initial-Boundary Value Problems | Method of Lines |
Área/s de conocimiento: | Matemática Aplicada |
Fecha de publicación: | 18-ene-2018 |
Editor: | Scientific Research Publishing |
Cita bibliográfica: | Cortés-Molina, M., Reyes, J.A. and García-Alonso, F. (2018) The G-functions Series Method Adapted to the Numerical Integration of Parabolic PDE. Journal of Applied Mathematics and Physics, 6, 161-173. https://doi.org/10.4236/jamp.2018.61016 |
Resumen: | 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. |
URI: | http://hdl.handle.net/10045/72728 |
ISSN: | 2327-4352 (Print) | 2327-4379 (Online) |
DOI: | 10.4236/jamp.2018.61016 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | © 2018 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.4236/jamp.2018.61016 |
Aparece en las colecciones: | INV - MMS - Artículos de Revistas |
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