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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi


IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

SCImago Journal Rank (SJR) 2017: 0.382
Source Normalized Impact per Paper (SNIP) 2017: 0.636

Mathematical Citation Quotient (MCQ) 2017: 0.12

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2191-0294
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Volume 19, Issue 7-8

Issues

Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three

Vijitha Mukundan / Ashish Awasthi
  • Corresponding author
  • Department of Mathematics, National Institute of Technology Calicut, Kozhikode 673 601, Kerala, India
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Published Online: 2018-10-23 | DOI: https://doi.org/10.1515/ijnsns-2017-0027

Abstract

We present an efficient numerical method for solving the nonlinear modified Burgers’ equation (MBE) using the multi-step method. The nonlinear MBE is first discretized along the spatial direction alone by using the method of lines technique, and this method converts the MBE to a nonlinear system of ordinary differential equations. Multistep methods are employed to solve the nonlinear system of ordinary differential equations. Applicability of the proposed numerical techniques is established through test examples. Discrete root mean square error norm (L2) and maximum error norm (L) are computed and presented for demonstrating the accuracy of the present numerical method. Numerical experiments supported by figures shows that the proposed numerical scheme shows excellent agreement with exact solution and is superior to some existing numerical methods.

Keywords: modified Burgers’ equation; method of lines; backward differentiation formulas

PACS: 65M06; 65M12

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About the article

Received: 2017-01-30

Accepted: 2018-10-06

Published Online: 2018-10-23

Published in Print: 2018-12-19


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 7-8, Pages 669–680, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2017-0027.

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