Implicit Finite Difference Solutions of One-Dimensional Burgers’ Equation Using Newton–HSSOR Method

J. Sulaiman (), M. K. Hasan (), M. Othman () and S.A.A. Karim ()
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J. Sulaiman: Universiti Malaysia Sabah, Mathematics with Economics Programme
M. K. Hasan: Universiti Kebangsaan Malaysia, School of Information Technology
M. Othman: Universiti Putra Malaysia, Department of Communication Technology and Network
S.A.A. Karim: Universiti Teknologi Petronas, Fundamental and Applied Sciences Department

A chapter in International Conference on Mathematical Sciences and Statistics 2013, 2014, pp 285-295 from Springer

Abstract: Abstract In this paper, we present the application of half-sweep successive over-relaxation (HSSOR) iterative methods together with Newton scheme, collectively Newton–HSSOR, in solving the nonlinear systems generated from the half-sweep Crank–Nicolson finite difference discretization scheme for a one-dimensional Burgers’ equation. To linearize nonlinear systems, the Newton scheme is proposed to transform the nonlinear system into the form of linear system. In addition to that, the basic formulation and implementation of Newton–HSSOR iterative method are also shown. For comparison purpose, we also consider combinations between the full-sweep Gauss–Seidel (FSGS) and full-sweep successive over-relaxation (FSSOR) iterative methods with Newton scheme, which are indicated as Newton–FSGS and Newton–FSSOR methods respectively. Consequently, two illustrative examples are included to demonstrate the validity and applicability of tested methods. Finally, it can be concluded that the Newton–HSSOR method shows superiority over other tested methods.

Keywords: Implicit Finite Difference Solution; Newton Scheme; Linear System; finite Difference Approximation Equation; Interior Nodal Points (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-4585-33-0_29

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DOI: 10.1007/978-981-4585-33-0_29

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