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Implicit finite difference solutions of one-dimensional Burgers’ equation using Newton-HSSOR method. (English) Zbl 1318.65057

Kilicman, Adem (ed.) et al., International conference on mathematical sciences and statistics 2013. Selected papers. ICMSS 2013, Kuala Lumpur, Malaysia, February 5–7, 2013. Singapore: Springer (ISBN 978-981-4585-32-3/hbk; 978-981-4585-33-0/ebook). 285-295 (2014).
Summary: 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.
For the entire collection see [Zbl 1286.00057].

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
35Q53 KdV equations (Korteweg-de Vries equations)
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