Sparse Wavelet Representation of Differential Operators with Piecewise Polynomial Coefficients

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F17%3A00005102" target="_blank" >RIV/46747885:24510/17:00005102 - isvavai.cz</a>
Result on the web
<a href="http://www.mdpi.com/2075-1680/6/1/4" target="_blank" >http://www.mdpi.com/2075-1680/6/1/4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/axioms6010004" target="_blank" >10.3390/axioms6010004</a>

Result language
angličtina
Original language name
Sparse Wavelet Representation of Differential Operators with Piecewise Polynomial Coefficients
Original language description
We propose a construction of a Hermite cubic spline-wavelet basis on the interval and hypercube. The basis is adapted to homogeneous Dirichlet boundary conditions. The wavelets are orthogonal to piecewise polynomials of degree at most seven on a uniform grid. Therefore, the wavelets have eight vanishing moments, and the matrices arising from discretization of differential equations with coefficients that are piecewise polynomials of degree at most four on uniform grids are sparse. Numerical examples demonstrate the efficiency of an adaptive wavelet method with the constructed wavelet basis for solving the one-dimensional elliptic equation and the two-dimensional Black-Scholes equation with a quadratic volatility.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA16-09541S" target="_blank" >GA16-09541S: Robust numerical schemes for pricing of selected options under various market conditions</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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