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Evolutionary Systems Representations Based on Later Time Samples and Applications to PDEs

Evolutionary Systems Representations Based on Later Time Samples and Applications to PDEs

Year:    2020

Author:    Yeon Hyang Kim, Roza Aceska

East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 838–850

Abstract

Let $\{ƒ_n\}^∞_{n=1}$ be a basis for $L_2([0, 1])$ and $\{g_n\}^∞_{n=1}$ be a system of functions of controlled decay on [0,∞). Considering a function u(x, t) that can be the represented in the form

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where an ∈ R, x ∈ [0, 1] and t ∈ [0,∞), we investigate whether the function ƒ(x) = u(x, 0) can be approximated, in a reasonable sense, by using data u(x0, t1), u(x0, t2),..., u(x0, tN). A mathematical framework and efficient computational schemes are developed to determine approximate solutions for various classes of partial differential equations via sampled data by first establishing a near-best approximation of ƒ .

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.210220.120620

East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 4 : pp. 838–850

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Dynamical system evolutionary systems representation near-best approximation initial data PDEs.

Author Details

Yeon Hyang Kim

Roza Aceska