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

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dc.contributor.author Černá, Dana
dc.contributor.author Finěk, Václav
dc.date.accessioned 2019-10-18T06:34:02Z
dc.date.available 2019-10-18T06:34:02Z
dc.date.issued 2019-10-18
dc.identifier.uri https://dspace.tul.cz/handle/15240/154036
dc.identifier.uri https://www.sciencedirect.com/science/article/pii/S0377042719303140
dc.description.abstract 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. cs
dc.format.extent 18 stran cs
dc.language.iso cs cs
dc.publisher ELSEVIER, RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS
dc.relation.ispartof JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
dc.subject Wavelet cs
dc.subject Quadratic spline cs
dc.subject Short support cs
dc.subject Galerkin method cs
dc.subject Integral equation cs
dc.subject Integro-differential equation cs
dc.title Galerkin method with new quadratic spline wavelets for integral and integro-differential equations cs
dc.identifier.doi 10.1016/j.cam.2019.06.033
local.relation.volume 363
local.citation.spage 426
local.citation.epage 443
local.identifier.publikace 7358


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