Book ChapterDOI
Splitting methods and their application to the abstract cauchy problems
István Faragó
- pp 35-45
TLDR
It is shown that the well-known fully-discretized numerical models elaborated to the numerical solution of the abstract Cauchy problem can be interpreted in this manner.Abstract:
In this paper we consider the interaction of the operator splitting method and applied numerical method to the solution of the different sub-processes. We show that the well-known fully-discretized numerical models (like Crank-Nicolson method, Yanenko method, sequential alternating Marchuk method, parallel alternating method, etc.), elaborated to the numerical solution of the abstract Cauchy problem can be interpreted in this manner. Moreover, on the base of this unified approach a sequence of the new methods can be defined and investigated.read more
Citations
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Book ChapterDOI
Application of the Method of Fractional Steps to Boundary Value Problems for Laplace’s and Poisson’s Equations
TL;DR: In this article, the Dirichlet problem in the rectangular region was considered, where γ is the boundary G, G = {0 < x i < π, i = 1, 2}.
Journal ArticleDOI
Iterative operator-splitting methods for linear problems
István Faragó,Jürgen Geiser +1 more
TL;DR: This paper suggests a new method which is based on the combination of the splitting time interval and the traditional iterative operator splitting, and analyses the local splitting error of the method.
Journal ArticleDOI
Advanced operator splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients
TL;DR: An efficient method to solve numerically the equations of dissipative dynamics of the binary phase-field crystal model proposed by Elder et al. is presented, which can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs is observed.
Journal ArticleDOI
Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations
TL;DR: In this article, the authors combine implicit Runge-Kutta and BDF with iterative operator-splitting methods to obtain higher-order time integrators for convection-diffusion reactions.
Journal ArticleDOI
Encapsulated formulation of the selective frequency damping method
TL;DR: In this article, an encapsulated formulation of the selective frequency damping method for finding unstable equilibria of dynamical systems is presented, which is particularly useful when analysing the stability of fluid flows.
References
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Journal ArticleDOI
Difference Methods for Initial-Value Problems.
Book
Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations
Willem Hundsdorfer,Jan Verwer +1 more
TL;DR: This paper presents a meta-modelling procedure called “Stabilized Explicit Runge-Kutta Methods”, which automates the very labor-intensive and therefore time-heavy and therefore expensive process of integrating discrete-time components into a coherent system.