Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions
In this work, the Finite Element Method is used for finding the numerical solution of an elliptic problem with Henstock–Kurzweil integrable functions. In particular, Henstock–Kurzweil high oscillatory functions were considered. The weak formulation of the problem leads to integrals that are calculat...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/8948570 |
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| author | D. A. León-Velasco M. M. Morín-Castillo J. J. Oliveros-Oliveros T. Pérez-Becerra J. A. Escamilla-Reyna |
| author_facet | D. A. León-Velasco M. M. Morín-Castillo J. J. Oliveros-Oliveros T. Pérez-Becerra J. A. Escamilla-Reyna |
| author_sort | D. A. León-Velasco |
| collection | DOAJ |
| description | In this work, the Finite Element Method is used for finding the numerical solution of an elliptic problem with Henstock–Kurzweil integrable functions. In particular, Henstock–Kurzweil high oscillatory functions were considered. The weak formulation of the problem leads to integrals that are calculated using some special quadratures. Definitions and theorems were used to guarantee the existence of the integrals that appear in the weak formulation. This allowed us to apply the above formulation for the type of slope bounded variation functions. Numerical examples were developed to illustrate the ideas presented in this article. |
| format | Article |
| id | doaj-art-cf5025494a6d46d89f48a2030af2e836 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-cf5025494a6d46d89f48a2030af2e8362025-02-03T06:08:31ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/89485708948570Numerical Solution of Some Differential Equations with Henstock–Kurzweil FunctionsD. A. León-Velasco0M. M. Morín-Castillo1J. J. Oliveros-Oliveros2T. Pérez-Becerra3J. A. Escamilla-Reyna4Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana Cuajimalpa, MexicoFacultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, MexicoFacultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, MexicoFacultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, MexicoFacultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, MexicoIn this work, the Finite Element Method is used for finding the numerical solution of an elliptic problem with Henstock–Kurzweil integrable functions. In particular, Henstock–Kurzweil high oscillatory functions were considered. The weak formulation of the problem leads to integrals that are calculated using some special quadratures. Definitions and theorems were used to guarantee the existence of the integrals that appear in the weak formulation. This allowed us to apply the above formulation for the type of slope bounded variation functions. Numerical examples were developed to illustrate the ideas presented in this article.http://dx.doi.org/10.1155/2019/8948570 |
| spellingShingle | D. A. León-Velasco M. M. Morín-Castillo J. J. Oliveros-Oliveros T. Pérez-Becerra J. A. Escamilla-Reyna Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions Journal of Function Spaces |
| title | Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions |
| title_full | Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions |
| title_fullStr | Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions |
| title_full_unstemmed | Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions |
| title_short | Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions |
| title_sort | numerical solution of some differential equations with henstock kurzweil functions |
| url | http://dx.doi.org/10.1155/2019/8948570 |
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