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Numerical Techniques for Unsteady Nonlinear Burgers Equation Based on Backward Differentiation Formulas

Numerical Techniques for Unsteady Nonlinear Burgers Equation Based on Backward Differentiation... AbstractWe introduce new numerical techniques for solving nonlinear unsteady Burgers equation. The numerical technique involves discretization of all variables except the time variable which converts nonlinear PDE into nonlinear ODE system. Stability of the nonlinear system is verified using Lyapunov’s stability criteria. Implicit stiff solvers backward differentiation formula of order one, two and three are used to solve the nonlinear ODE system. Four test problems are included to show the applicability of introduced numerical techniques. Numerical solutions so obtained are compared with solutions of existing schemes in literature. The proposed numerical schemes are found to be simple, accurate, fast, practical and superior to some existing methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

Numerical Techniques for Unsteady Nonlinear Burgers Equation Based on Backward Differentiation Formulas

Nonlinear Engineering , Volume 7 (3): 11 – Sep 25, 2018

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References (43)

Publisher
de Gruyter
Copyright
© 2017 Walter de Gruyter GmbH, Berlin/Boston
ISSN
2192-8029
eISSN
2192-8029
DOI
10.1515/nleng-2017-0068
Publisher site
See Article on Publisher Site

Abstract

AbstractWe introduce new numerical techniques for solving nonlinear unsteady Burgers equation. The numerical technique involves discretization of all variables except the time variable which converts nonlinear PDE into nonlinear ODE system. Stability of the nonlinear system is verified using Lyapunov’s stability criteria. Implicit stiff solvers backward differentiation formula of order one, two and three are used to solve the nonlinear ODE system. Four test problems are included to show the applicability of introduced numerical techniques. Numerical solutions so obtained are compared with solutions of existing schemes in literature. The proposed numerical schemes are found to be simple, accurate, fast, practical and superior to some existing methods.

Journal

Nonlinear Engineeringde Gruyter

Published: Sep 25, 2018

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