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An exploration of quintic Hermite splines to solve Burgers’ equation

  • Shelly Arora
  • Inderpreet KaurEmail author
  • Wudneh Tilahun
Open Access
Article
  • 65 Downloads

Abstract

An innovative scheme of collocation having quintic Hermite splines as base functions has been followed to solve Burgers’ equation. The scheme relies on approximation of Burgers’ equation directly in non-linear form without using Hopf–Cole transformation (Hopf in Commun Pure Appl Math 3:201–216, 1950; Cole in Q Appl Math 9:225–236, 1951). The significance of the numerical technique is demonstrated by comparing the numerical results to the exact solution and published results (Asaithambi in Appl Math Comput 216:2700–2708, 2010; Mittal and Jain in Appl Math Comput 218:7839–7855, 2012). Five problems with different initial conditions have been examined to validate the efficiency and accuracy of the scheme. Euclidean and supremum norms have been reckoned to scrutinize the stability of the numerical scheme. Results have been demonstrated in plane and surface plots to indicate the effectiveness of the scheme.

Mathematics Subject Classification

35B25 65N35 65N12 

Notes

Acknowledgements

Mrs. Inderpreet Kaur is thankful to DST for providing INSPIRE fellowship (IF140424).

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© The Author(s) 2019

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of MathematicsPunjabi UniversityPatialaIndia
  2. 2.Department of MathematicsDebre Tabor UniversityDebre TaborEthiopia

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