Boundary value problem for elliptic equations, a differential transformation approach
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
Boundary value problem for elliptic equations, a differential transformation approach
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
Boundary value problem for elliptic equations, a differential transformation approach
Popis výsledku anglicky
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.
Klasifikace
Druh
D - Stať ve sborníku
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
S - Specificky vyzkum na vysokych skolach
Ostatní
Rok uplatnění
2019
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název statě ve sborníku
International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2018.
ISBN
9780735418547
ISSN
0094-243X
e-ISSN
—
Počet stran výsledku
4
Strana od-do
1-4
Název nakladatele
Neuveden
Místo vydání
neuveden
Místo konání akce
Ixia, Rhodes
Datum konání akce
13. 9. 2018
Typ akce podle státní příslušnosti
WRD - Celosvětová akce
Kód UT WoS článku
000521108600312