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.
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