Implicit ODE solvers with good local error control for the transient analysis of Markov models

DOI10.1016/j.amc.2016.08.009zbMath1411.65092OpenAlexW2516674495MaRDI QIDQ1737142

Juan Antonio Carrasco, Víctor Suñé

Publication date: 27 March 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2117/89791

zbMATH Keywords

continuous-time Markov chainsimplicit ODE solverstransient analysis

Mathematics Subject Classification ID

Numerical analysis or methods applied to Markov chains (65C40) Numerical methods for initial value problems involving ordinary differential equations (65L05) Continuous-time Markov processes on discrete state spaces (60J27)

Uses Software

• Expokit
• Maple
• SUNDIALS
• TR-BDF2
• RODAS
• CGS
• ILUT

Cites Work

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• SUNDIALS
• Numerical transient analysis of Markov models
• A lower bound for the smallest singular value of a matrix
• On recurring theorems on diagonal dominance
• A numerical study of large sparse matrix exponentials arising in Markov chains.
• Analysis and implementation of TR-BDF2
• Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf Wärmeleitungsprobleme
• A computationally efficient technique for transient analysis of repairable Markovian systems
• The Randomization Technique as a Modeling Tool and Solution Procedure for Transient Markov Processes
• Inexact Uniformization Method for Computing Transient Distributions of Markov Chains
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Transient analysis of acyclic markov chains
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations
• Expokit
• Adaptive uniformization
• A Unified Proof for the Convergence of Jacobi and Gauss–Seidel Methods
• ILUT: A dual threshold incomplete LU factorization
• Convergence Properties of the Spline Fit
• A class ofA-stable methods
• Implicit Runge-Kutta Processes
• A special stability problem for linear multistep methods
• Matrix Iterative Analysis

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