 An efficient collocation method based on Hermite formula and cubic B-splines for numerical solution of the Burgers’ equationMuhammad Abdullah, Muhammad Yaseen and Manuel De la Sen Mathematics and Computers in Simulation (MATCOM), 2022, vol. 197, issue C, 166-184 Abstract: In this paper, an efficient computational technique for the numerical solution of the Burgers’ equation (BE) is presented. The derivative in space is approximated using cubic B-splines and the Hermite formula whereas time discretization is performed by finite differences. The stability of the proposed scheme is derived using the standard von Neumann method to establish the fact that the errors do not amplify. Convergence analysis for the proposed scheme is also discussed. A sufficiently smooth piecewise continuous function is obtained as an approximation to the exact solution which enables us to approximate the solution at any wanted position in the domain. Numerical tests are carried out to further confirm the accuracy and stability of the method. The outcomes of this study are compared with those previously presented in literature. Keywords: Burgers’ equation; Cubic B-splines; Hermite formula; Stability; Convergence (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:197:y:2022:i:c:p:166-184 DOI: 10.1016/j.matcom.2022.02.013 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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