title: Construction of implicit multistep methods for solving integral algebraic equations
metadata.name: dc.contributor.author
metadata.value: Bulatov, Mikhail V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Hadizadeh, Mahmoud
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Chistyakova, Elena V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-10-18T11:54:40Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-10-18T11:54:40Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Bulatov M. V., Hadizadeh M., Chistyakova E. V. Construction of implicit multistep methods for solving integral algebraic equations. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2019, vol. 15, iss. 3, pp. 310–322.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu10.2019.302
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16383
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This paper discusses techniques for construction of implicit stable multistep methods for solving systems of linear Volterra integral equations with a singular matrix multiplying the leading part, which means that systems under consideration comprise Volterra equations of the first kind as well as Volterra equations of the second kind. Methods for solving first kind Volterra equations so far have been justified only for some special cases, for example, for linear equations with a kernel that does not vanish on the diagonal for all points of the segment. We present a theoretical analysis of solvability of the systems under study, single out classes of two- and three-step numerical methods of order two and three, respectively, and provide examples to illustrate our theoretical assumptions. The experimental results indicate that the stability of the methods can be controlled by some weight parameter that should be chosen from a prescribed interval to provide the necessary stability of the algorithms.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: M. V. Bulatov and E. V. Chistyakova acknowledge the financial support from the Russian Foundation
  for Basic Research (projects N 18-51-54001, 18-01-00643, 18-29-10019).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 15; Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: system of Volterra equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral algebraic equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: multistep method
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: quadrature formulas, stability analysis
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Construction of implicit multistep methods for solving integral algebraic equations
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 310-322.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16383/1/310-322.pdf
resources.format: Adobe PDF
resources.size: 681,38 kB