Applications of Magnus expansions and pseudospectra to Markov processes

Autor:	Shev MacNamara, Arieh Iserles
Rok vydání:	2018
Předmět:	Process (engineering) Computer science Applied Mathematics Numerical analysis Markov process 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics symbols.namesake Master equation symbols Applied mathematics 0101 mathematics Eigenvalues and eigenvectors
Zdroj:	European Journal of Applied Mathematics. 30:400-425
ISSN:	1469-4425 0956-7925
DOI:	10.1017/s0956792518000177
Popis:	Copyright © 2018 Cambridge University Press. New directions in Markov processes and research on master equations are showcased by example. The utility of Magnus expansions for handling time-varying rates is demonstrated. The useful notion in applied mathematics often turns out to be the pseudospectra and not simply the eigenvalues. We highlight that general principle with our own examples of Markov processes where exact eigenvalues are found and contrasted with the large errors produced by standard numerical methods. As a motivating application, isomerisation provides a running example and an illustration of our approaches to chemical kinetics. We also present a brief example of a totally asymmetric exclusion process.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d3b3015c838c947a6be90655184fda4a https://doi.org/10.1017/s0956792518000177 Zobrazit plný text záznamu