Adaptive cellular integration of linearly implicit differential equations
type: Item
instance of: scholarly article
title: Adaptive cellular integration of linearly implicit differential equations
zbMATH Open document ID: 0941.65127
DOI: 10.1016/S0377-0427(99)00151-X
author: Ricardo Riaza
author: Pedro J. Zufiria
published in: Journal of Computational and Applied Mathematics
publication date: 2000-07-20T00:00:00Z
review text: The paper illustrates the use of cell mapping methods for the global analysis of linearly implicit ordinary differential equations. These equations can possess some points where standard cellular techniques can not be applied, motivating the use of adaptive tools. The difficulties encountered with the new method are formalized within a finite-time convergence model. Numerical experiments illustrate the scope of the cellular integration method.
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M15
zbMATH DE Number: 1398838
zbMATH Keywords: linearly implicit ordinary differential equations
zbMATH Keywords: spatial discretization
zbMATH Keywords: adaptive cellular integration
zbMATH Keywords: global analysis
zbMATH Keywords: cell mapping methods
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
reviewed by: Dana Petcu
MaRDI profile type: Publication
cites work: Markov Partitions for Axiom A Diffeomorphisms
cites work: Q4164074
cites work: Spatial discretization of mappings
cites work: Basin of attraction of cycles of discretizations of dynamical systems with SRB invariant measures.
cites work: Monotonic dynamical systems under spatial discretization
cites work: Q5751211
cites work: Do numerical orbits of chaotic dynamical processes represent true orbits?
cites work: An Unravelling Algorithm for Global Analysis of Dynamical Systems: An Application of Cell-to-Cell Mappings
cites work: Cell-to-cell mapping. A method of global analysis for nonlinear systems
cites work: Informal Remarks on the Orbit Structure of Discrete Approximations to Chaotic Maps
cites work: Optimal control of non-linear systems through hybrid cell-mapping/artificial-neural-networks techniques
cites work: Q4872274
cites work: Chaos in the Lorenz equations: a computer-assisted proof
cites work: Chaos in the Lorenz equations: A computer assisted proof. Part II: Details
cites work: Q5652137
cites work: Global aspects of the continuous and discrete Newton method: A case study
cites work: Implicit differential equations near a singular point
cites work: On the Computation of Impasse Points of Quasi-Linear Differential-Algebraic Equations
cites work: On Newton’s Method for Singular Problems
cites work: Structurally stable differential systems of the form \(A(x)x'=F(x)\)
cites work: Q4336193
cites work: Q4023802
cites work: Q4333039
cites work: Interpolated Cell Mapping of Dynamical Systems
cites work: A computational method for finding all the roots of a vector function
Wikidata QID: Q127724706
full work available at URL: s0377-0427(99)00151-x
OpenAlex ID: W2012019520
Recommended article: Adaptively weighted numerical integration in the finite cell method
Recommended article: Q3138301
Recommended article: Q4530536
Recommended article: Adaptive computational methods for differential equations
Recommended article: Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting
Recommended article: Adaptive integration of stiff ODE
Recommended article: Adaptive methods for numerical integration in problems of dynamical system simulation
Recommended article: Q4797885
Recommended article: Q3189319
Recommended article: A self-adaptive time integration algorithm for solving partial differential equations
description: scientific article; zbMATH DE number 1398838