A NEW LEGENDRE POLYNOMIAL-BASED APPROACH FOR NON-AUTONOMOUS LINEAR ODES

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493292" target="_blank" >RIV/00216208:11320/24:10493292 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=MfRUV0NdP0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=MfRUV0NdP0</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1553/etna_vol60s292" target="_blank" >10.1553/etna_vol60s292</a>

Result language
angličtina
Original language name
A NEW LEGENDRE POLYNOMIAL-BASED APPROACH FOR NON-AUTONOMOUS LINEAR ODES
Original language description
We introduce a new method with spectral accuracy to solve linear non-autonomous ordinary differential equations (ODEs) of the kind dtd ũ(t) = f(t)ũ(t), ũ(-1) = 1, with f(t) an analytic function. The method is based on a new analytical expression for the solution ũ(t) given in terms of a convolution-like operation, the ?-product. We prove that, by representing this expression in a finite Legendre polynomial basis, the solution ũ(t) can be found by solving a matrix problem involving the Fourier coefficients of f(t). An efficient procedure is proposed to approximate the Legendre coefficients of ũ(t), and the truncation error and convergence are analyzed. We show the effectiveness of the proposed procedure through numerical experiments. Our approach allows for a generalization of the method to solve systems of linear ODEs.
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
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OECD FORD branch
10102 - Applied mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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