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.
Izadi, M. (2020). Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation. Computational Methods for Differential Equations, 8(4), 708-732. doi: 10.22034/cmde.2020.32615.1513
MLA
Mohammad Izadi. "Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation". Computational Methods for Differential Equations, 8, 4, 2020, 708-732. doi: 10.22034/cmde.2020.32615.1513
HARVARD
Izadi, M. (2020). 'Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation', Computational Methods for Differential Equations, 8(4), pp. 708-732. doi: 10.22034/cmde.2020.32615.1513
VANCOUVER
Izadi, M. Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation. Computational Methods for Differential Equations, 2020; 8(4): 708-732. doi: 10.22034/cmde.2020.32615.1513
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