University of Tabriz Computational Methods for Differential Equations 2345-3982 8 4 2020 11 01 Applications of the Newton-Raphson method in a SDFEM for inviscid Burgers equation 708 732 9920 10.22034/cmde.2020.32615.1513 EN Mohammad Izadi Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran Journal Article 2019 03 19 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. https://cmde.tabrizu.ac.ir/article_9920_6b55937eecf255da25814ed38b43bd59.pdf