×

The convergence of approximate solutions of the Cauchy problem for the model of quasi-steady process in conducting nondispersive medium with relaxation. (English) Zbl 1359.65141

Author’s abstract: This article deals with numerical method for solving of the Dirichlet-Cauchy problem for equation modeling the quasi-steady process in conducting nondispersive medium with relaxation. This problem describes a complex electrodynamic process, allows to consider and predict its flow in time. The study of electrodynamic models is necessary for the development of electrical engineering and new energy saving technologies. The main equation of the model is considered as a quasi-linear Sobolev type equation. The convergence of approximate solutions obtained from the use of the method of straight lines with \(\varepsilon\)-embedding method and complex Rosenbrock method is proven in the article. The lemmas on the local error and on the distribution of error are proven. Estimates of a global error of the method are obtained.

MSC:

65L80 Numerical methods for differential-algebraic equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65J15 Numerical solutions to equations with nonlinear operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] [1] М.О. Корпусов, Ю.Д. Плетнер, А.Г. Свешников, ”О квазистационарных процессах в проводящих средах без дисперсии”, Ж. вычисл. матем. и матем. физ., 40:8 (2000), 1237–1249 · Zbl 0993.78013
[2] [2] М.О. Корпусов, ””Разрушение” решения псевдопараболического уравнения с производной по времени от нелинейного эллиптического оператора”, Ж. вычисл. матем. и матем. физ., 42:12 (2002), 1788–1795 · Zbl 1116.35336
[3] [3] А.Г. Свешников, A.Б. Альшин, М.О. Корпусов, Нелинейный функциональный анализ и его приложения к уравнениям в частных производных, Науч. мир, Москва, 2008, ISBN: 978-5-91522-011-8, 399 с. · Zbl 0342.02023
[4] [4] E. A. Bogatyreva, ”Numerical modeling of quasi-steady process in conducting nondispersive medium with relaxation”, J. Comp. Eng. Math., 2:1 (2015), 45–51 · Zbl 1338.78021
[5] [5] А.Б. Альшин, Е.А. Альшина, Н.Н. Калиткин, А.Б. Корягина, ”Схемы Розенброка с комплексными коэффициентами для жестких и дифференциально-алгебраических систем”, Ж. вычисл. матем. и матем. физ., 46:8 (2006), 1392–1414 · Zbl 1204.11080
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.