Numerical solution of burger-huxley second order partial differential equations using splines

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we are concerned about numerical solutions to ODEs and PDEs that are used to model and describe real-life problems. Usually, these equations are approximated numerically because it is convenient and on-hand to be calculated on computing devices. The Burger-Huxley partial differential equations model the interaction between reactions, diffusion, and convection besides other phenomenas in liquid crystals. Numerically, the Burger-Huxley equations have been solved using the quadrature technique, homotopy perturbation, finite-difference, and B-spline quasi-interpolation methods. Many existing numerical methods have ill-conditioned matrices. Our aim is to develop a numerical algorithm based on the use of splines and their derivatives without requiring the solution of the resulting system that might be ill-conditioned. The method will be applied to initial value-boundary value problems. Special technique will be improved for the Burger-Huxley equations. It is anticipated that the approximate solution of the IV-BV problems has significant accuracy and efficiency.

Original languageEnglish
Title of host publicationInternational Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
EditorsTheodore E. Simos, Theodore E. Simos, Theodore E. Simos, Theodore E. Simos, Theodore E. Simos, Charalambos Tsitouras
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735440258
DOIs
Publication statusPublished - Nov 24 2020
EventInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019 - Rhodes, Greece
Duration: Sep 23 2019Sep 28 2019

Publication series

NameAIP Conference Proceedings
Volume2293
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
Country/TerritoryGreece
CityRhodes
Period9/23/199/28/19

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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