Temat: error estimate - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition
Autorzy:: Sekar, Elango
Tamilselvan, Ayyadurai
Powiązania:: https://bibliotekanauki.pl/articles/122568.pdf
Data publikacji:: 2019
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: singular perturbation problem
finite difference scheme
delay
integral boundary condition
error estimate
schemat różnic skończonych
opóźnienie
oszacowanie błędu
metoda numeryczna
metoda równań skończonych
Opis:: A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 99-110
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: A direct and accurate adaptive semi-Lagrangian scheme for the Vlasov-Poisson equation
Autorzy:: Campos Pinto, M.
Powiązania:: https://bibliotekanauki.pl/articles/929689.pdf
Data publikacji:: 2007
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: metoda Lagrangiana
oszacowanie błędu
szybkość zbieżności
fully adaptive scheme
semi-Lagrangian method
Vlasov-Poisson equation
error estimate
convergence rates
optimal transport of adaptive multiscale meshes
Opis:: This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1 + 1)- dimensional Vlasov-Poisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis are also given, which yield the first error estimate for an adaptive scheme in the context of the Vlasov equation. This article focuses on a key feature of our method, which is a new algorithm to transport multiscale meshes along a smooth flow, in a way that can be said optimal in the sense that it satisfies both accuracy and complexity estimates which are likely to lead to optimal convergence rates for the whole numerical scheme. From the regularity analysis of the numerical solution and how it gets transported by the numerical flow, it is shown that the accuracy of our scheme is monitored by a prescribed tolerance parameter \epsilon which represents the local interpolation error at each time step. As a consequence, the numerical solutions are proved to converge in L\infty towards the exact ones as \epsilon and \delta t tend to zero, and in addition to the numerical tests presented in (Campos Pinto and Mehrenberger, 2007), some complexity bounds are established which are likely to prove the optimality of the meshes.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 351-359
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

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