Wavelet-Galerkin Method for Second-Order Integro-Differential Equations on Product Domains

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F21%3A00008551" target="_blank" >RIV/46747885:24510/21:00008551 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.springer.com/gp/book/9783030655082" target="_blank" >https://www.springer.com/gp/book/9783030655082</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-65509-9" target="_blank" >10.1007/978-3-030-65509-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Wavelet-Galerkin Method for Second-Order Integro-Differential Equations on Product Domains

Popis výsledku v původním jazyce

The chapter deals with the study of the wavelet-Galerkin method for the numerical solution of the second-order partial integro-differential equations on the product domains. Prescribed boundary conditions are of Dirichlet or Neumann type on each facet of the domain. The variational formulation is derived and the existence and uniqueness of the weak solution are discussed. Multi-dimensional wavelet bases satisfying boundary conditions are constructed by the tensor product of wavelet bases on the interval using an isotropic and anisotropic approaches. The constructed wavelet bases are used in the Galerkin method to find the numerical solution of the integro-differential equations. The convergence of the method is proven and error estimates are derived. The advantage of the method consists in the uniform boundedness of the condition numbers of discretization matrices and in the fact that these matrices exhibit an exponential decay of their elements away from the main diagonal. Based on the decay estimates we propose a compression strategy for approximation of the discretization matrices by sparse or quasi-sparse matrices. Numerical experiments are presented to confirm the theoretical results and to illustrate the efficiency and applicability of the method.

Název v anglickém jazyce

Wavelet-Galerkin Method for Second-Order Integro-Differential Equations on Product Domains

Popis výsledku anglicky

The chapter deals with the study of the wavelet-Galerkin method for the numerical solution of the second-order partial integro-differential equations on the product domains. Prescribed boundary conditions are of Dirichlet or Neumann type on each facet of the domain. The variational formulation is derived and the existence and uniqueness of the weak solution are discussed. Multi-dimensional wavelet bases satisfying boundary conditions are constructed by the tensor product of wavelet bases on the interval using an isotropic and anisotropic approaches. The constructed wavelet bases are used in the Galerkin method to find the numerical solution of the integro-differential equations. The convergence of the method is proven and error estimates are derived. The advantage of the method consists in the uniform boundedness of the condition numbers of discretization matrices and in the fact that these matrices exhibit an exponential decay of their elements away from the main diagonal. Based on the decay estimates we propose a compression strategy for approximation of the discretization matrices by sparse or quasi-sparse matrices. Numerical experiments are presented to confirm the theoretical results and to illustrate the efficiency and applicability of the method.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Topics in Integral and Integro-Differential Equations

ISBN

978-3-030-65508-2

Počet stran výsledku

40

Strana od-do

1-40

Počet stran knihy

255

Název nakladatele

Springer International Publishing

Místo vydání

Switzerland

Kód UT WoS kapitoly

—