Classification of Difference Schemes of Maximum Possible Accuracy on Extended Symmetric Stencils for the Schrödinger Equation and the Heat Conduction Equation

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Classification of Difference Schemes of Maximum Possible Accuracy on Extended Symmetric Stencils for the Schrödinger Equation and the Heat Conduction Equation. / Paasonen, V. I.

In: Numerical Analysis and Applications, Vol. 13, No. 1, 01.02.2020, p. 82-94.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{cf9f02d42cea4c1e842d214b9f95e9b4,

title = "Classification of Difference Schemes of Maximum Possible Accuracy on Extended Symmetric Stencils for the Schr{\"o}dinger Equation and the Heat Conduction Equation",

abstract = "All possible symmetric two-level difference schemes on arbitraryextended stencils are considered for the Schr{\"o}dinger equation and forthe heat conduction equation. The coefficients of the schemes are foundfrom conditions under which the maximum possible order of approximationwith respect to the main variable is attained. A class of absolutelystable schemes is considered in a set of maximally exact schemes. Toinvestigate the stability of the schemes, the von Neumann criterion isverified numerically and analytically. It is proved that the schemes areabsolutely stable or unstable depending on the order of approximationwith respect to the evolution variable. As a result of theclassification, absolutely stable schemes up to the tenth order ofaccuracy with respect to the main variable have been constructed.",

author = "Paasonen, {V. I.}",

year = "2020",

month = feb,

day = "1",

doi = "10.1134/S1995423920010073",

language = "English",

volume = "13",

pages = "82--94",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Classification of Difference Schemes of Maximum Possible Accuracy on Extended Symmetric Stencils for the Schrödinger Equation and the Heat Conduction Equation

AU - Paasonen, V. I.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - All possible symmetric two-level difference schemes on arbitraryextended stencils are considered for the Schrödinger equation and forthe heat conduction equation. The coefficients of the schemes are foundfrom conditions under which the maximum possible order of approximationwith respect to the main variable is attained. A class of absolutelystable schemes is considered in a set of maximally exact schemes. Toinvestigate the stability of the schemes, the von Neumann criterion isverified numerically and analytically. It is proved that the schemes areabsolutely stable or unstable depending on the order of approximationwith respect to the evolution variable. As a result of theclassification, absolutely stable schemes up to the tenth order ofaccuracy with respect to the main variable have been constructed.

AB - All possible symmetric two-level difference schemes on arbitraryextended stencils are considered for the Schrödinger equation and forthe heat conduction equation. The coefficients of the schemes are foundfrom conditions under which the maximum possible order of approximationwith respect to the main variable is attained. A class of absolutelystable schemes is considered in a set of maximally exact schemes. Toinvestigate the stability of the schemes, the von Neumann criterion isverified numerically and analytically. It is proved that the schemes areabsolutely stable or unstable depending on the order of approximationwith respect to the evolution variable. As a result of theclassification, absolutely stable schemes up to the tenth order ofaccuracy with respect to the main variable have been constructed.

UR - http://www.scopus.com/inward/record.url?scp=85080072366&partnerID=8YFLogxK

U2 - 10.1134/S1995423920010073

DO - 10.1134/S1995423920010073

M3 - Article

AN - SCOPUS:85080072366

VL - 13

SP - 82

EP - 94

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 1

ER -

ID: 23668395