Wavelet-Galerkin Method for Second-Order Integro-Differential Equations on Product Domains
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Wavelet-Galerkin Method for Second-Order Integro-Differential Equations on Product Domains
Original language description
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.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Topics in Integral and Integro-Differential Equations
ISBN
978-3-030-65508-2
Number of pages of the result
40
Pages from-to
1-40
Number of pages of the book
255
Publisher name
Springer International Publishing
Place of publication
Switzerland
UT code for WoS chapter
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