Boundary value problem for elliptic equations, a differential transformation approach
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F19%3APU132904" target="_blank" >RIV/00216305:26220/19:PU132904 - isvavai.cz</a>
Result on the web
<a href="https://aip.scitation.org/doi/10.1063/1.5114320" target="_blank" >https://aip.scitation.org/doi/10.1063/1.5114320</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.5114320" target="_blank" >10.1063/1.5114320</a>
Alternative languages
Result language
angličtina
Original language name
Boundary value problem for elliptic equations, a differential transformation approach
Original language description
In this paper, we propose an idea how the differential transformation, a semi-analytical approach based on Taylor’s theorem, can be used to find an approximation of the unique solution to the boundary value problem for partial differential equations of elliptic type. We focus on two-dimensional equations with initial conditions given at the sides of a square. The considered differential equation is transformed into a recurrence relation in two variables. Solving the recurrence relation using the boundary conditions leads to an infinite system of linear equations with infinitely many variables. Approximation of the solution is given in the form of two-dimensional Taylor polynomial whose coefficients are determined by solution to a truncated system of linear equations. Boundary value problem consisting of the Laplace equation and Dirichlet boundary conditions has been chosen to demonstrate relevance of the idea to the given problem.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2018.
ISBN
9780735418547
ISSN
0094-243X
e-ISSN
—
Number of pages
4
Pages from-to
1-4
Publisher name
Neuveden
Place of publication
neuveden
Event location
Ixia, Rhodes
Event date
Sep 13, 2018
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000521108600312