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Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation | ||
| Computational Methods for Differential Equations | ||
| مقاله 7، دوره 8، شماره 4، بهمن 2020، صفحه 708-732 اصل مقاله (785.25 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.32615.1513 | ||
| نویسنده | ||
| Mohammad Izadi* | ||
| Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| In this paper we investigate in detail the applications of the classical Newton-Raphson method in connection with a space-time finite element discretization scheme for the inviscid Burgers equation in one dimensional space. The underlying discretization method is the so-called streamline diffusion method, which combines good stability properties with high accuracy. The coupled nonlinear algebraic equations thus obtained in each space-time slab are solved by the generalized Newton-Raphson method. Exploiting the band-structured properties of the Jacobian matrix, two different algorithms based on the Newton-Raphson linearization are proposed. In a series of examples, we show that in each time-step a quadratic convergence order is attained when the Newton-Raphson procedure applied to the corresponding system of nonlinear equations. | ||
| کلیدواژهها | ||
| Finite element method؛ Burgers equation؛ Newton-Raphson method | ||
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