Galerkin method with new quadratic spline wavelets for integral and integro-differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F20%3A00007358" target="_blank" >RIV/46747885:24510/20:00007358 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0377042719303140" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0377042719303140</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2019.06.033" target="_blank" >10.1016/j.cam.2019.06.033</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Galerkin method with new quadratic spline wavelets for integral and integro-differential equations

Popis výsledku v původním jazyce

The paper is concerned with the wavelet-Galerkin method for the numerical solution of Fredholm linear integral equations and second-order integro-differential equations. We propose a construction of a quadratic spline-wavelet basis on the unit interval, such that the wavelets have three vanishing moments and the shortest support among such wavelets. We prove that this basis is a Riesz basis in the space L-2(0, 1). We adapt the basis to homogeneous Dirichlet boundary conditions, and using a tensor product we construct a wavelet basis on the hyperrectangle. We use the wavelet-Galerkin method with the constructed bases for solving integral and integro-differential equations, and we show that the matrices arising from discretization have uniformly bounded condition numbers and that they can be approximated by sparse matrices. We present numerical examples and compare the results with the Galerkin method using other quadratic spline wavelet bases and other methods.

Název v anglickém jazyce

Galerkin method with new quadratic spline wavelets for integral and integro-differential equations

Popis výsledku anglicky

The paper is concerned with the wavelet-Galerkin method for the numerical solution of Fredholm linear integral equations and second-order integro-differential equations. We propose a construction of a quadratic spline-wavelet basis on the unit interval, such that the wavelets have three vanishing moments and the shortest support among such wavelets. We prove that this basis is a Riesz basis in the space L-2(0, 1). We adapt the basis to homogeneous Dirichlet boundary conditions, and using a tensor product we construct a wavelet basis on the hyperrectangle. We use the wavelet-Galerkin method with the constructed bases for solving integral and integro-differential equations, and we show that the matrices arising from discretization have uniformly bounded condition numbers and that they can be approximated by sparse matrices. We present numerical examples and compare the results with the Galerkin method using other quadratic spline wavelet bases and other methods.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA16-09541S" target="_blank" >GA16-09541S: Robustní numerická schémata pro oceňování vybraných opcí za různých tržních podmínek</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

ISSN

0377-0427

e-ISSN

—

Svazek periodika

363

Číslo periodika v rámci svazku

JAN 2020

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

18

Strana od-do

426-443

Kód UT WoS článku

000488995600027

EID výsledku v databázi Scopus

2-s2.0-85068379426