Volume 10, Issue 4
Evolutionary Systems Representations Based on Later Time Samples and Applications to PDEs

Yeon Hyang Kim & Roza Aceska

East Asian J. Appl. Math., 10 (2020), pp. 838-850.

Published online: 2020-08

Preview Purchase PDF 9 738
Export citation
  • Abstract

Let {ƒn}n=1 be a basis for L2([0, 1]) and {gn}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

image.png

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 .

  • Keywords

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

  • AMS Subject Headings

35R30, 35A25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-10-838, author = {Yeon Hyang Kim , and Roza Aceska , }, title = {Evolutionary Systems Representations Based on Later Time Samples and Applications to PDEs}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {4}, pages = {838--850}, abstract = {

Let {ƒn}n=1 be a basis for L2([0, 1]) and {gn}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

image.png

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 .

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.210220.120620 }, url = {http://global-sci.org/intro/article_detail/eajam/17965.html} }
TY - JOUR T1 - Evolutionary Systems Representations Based on Later Time Samples and Applications to PDEs AU - Yeon Hyang Kim , AU - Roza Aceska , JO - East Asian Journal on Applied Mathematics VL - 4 SP - 838 EP - 850 PY - 2020 DA - 2020/08 SN - 10 DO - http://doi.org/10.4208/eajam.210220.120620 UR - https://global-sci.org/intro/article_detail/eajam/17965.html KW - Dynamical system, evolutionary systems representation, near-best approximation, initial data, PDEs. AB -

Let {ƒn}n=1 be a basis for L2([0, 1]) and {gn}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

image.png

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 .

Yeon Hyang Kim & Roza Aceska. (2020). Evolutionary Systems Representations Based on Later Time Samples and Applications to PDEs. East Asian Journal on Applied Mathematics. 10 (4). 838-850. doi:10.4208/eajam.210220.120620
Copy to clipboard
The citation has been copied to your clipboard