Detail publikačního výsledku

Boundary value problem for elliptic equations, a differential transformation approach

REBENDA, J.; ŠMARDA, Z.

Originální název

Boundary value problem for elliptic equations, a differential transformation approach

Anglický název

Boundary value problem for elliptic equations, a differential transformation approach

Druh

Stať ve sborníku v databázi WoS či Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Differential transformation; boundary value problem; partial differential equation

Klíčová slova v angličtině

Differential transformation; boundary value problem; partial differential equation

Autoři

REBENDA, J.; ŠMARDA, Z.

Rok RIV

2020

Vydáno

25.07.2019

ISBN

9780735418547

Kniha

International Conference of Numerical Analysis and Applied Mathematics, ICNAAM 2018.

ISSN

0094-243X

Periodikum

AIP conference proceedings

Svazek

2116

Číslo

310013

Stát

Spojené státy americké

Strany od

1

Strany do

4

Strany počet

4

URL

https://aip.scitation.org/doi/10.1063/1.5114320

BibTex

@inproceedings{BUT157985,
  author="Josef {Rebenda} and Zdeněk {Šmarda}",
  title="Boundary value problem for elliptic equations,  a differential  transformation approach",
  booktitle="International Conference of Numerical  Analysis and Applied Mathematics, ICNAAM 2018.",
  year="2019",
  journal="AIP conference proceedings",
  volume="2116",
  number="310013",
  pages="1--4",
  doi="10.1063/1.5114320",
  isbn="9780735418547",
  issn="0094-243X",
  url="https://aip.scitation.org/doi/10.1063/1.5114320"
}