Journal of Function Spaces (Jan 2019)

Numerical Solution of Some Differential Equations with Henstock–Kurzweil Functions

  • D. A. León-Velasco,
  • M. M. Morín-Castillo,
  • J. J. Oliveros-Oliveros,
  • T. Pérez-Becerra,
  • J. A. Escamilla-Reyna

DOI
https://doi.org/10.1155/2019/8948570
Journal volume & issue
Vol. 2019

Abstract

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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.