Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Anatoly A. Alikhanov"'
Publikováno v:
Applied Numerical Mathematics. 172:546-565
The paper aims to develop the stable numerical schemes for generalized time-fractional diffusion equations (GTFDEs) with smooth and non-smooth solutions on the non-uniform grid. In time, the generalized Caputo derivative is discretized by a differenc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::096d94caca7929bf5715614cce9a3ecd
https://doi.org/10.1016/j.apnum.2021.11.006
https://doi.org/10.1016/j.apnum.2021.11.006
Publikováno v:
International Journal of Computational Methods. 20
This paper represents a new application of Legendre wavelet and interpolating scaling function to discuss the approximate solution of variable order integro-differential equation having weakly singular kernel. So far, this technique has been used to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f7d0820424f139236eccbd6c47fd0f72
https://doi.org/10.1142/s0219876222500463
https://doi.org/10.1142/s0219876222500463
Publikováno v:
Applied Numerical Mathematics. 167:218-236
In this paper, we introduce a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel. This method is particularly suitable for problems whose solu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5148391b46d3461503ae588093133de7
https://doi.org/10.1016/j.apnum.2021.05.006
https://doi.org/10.1016/j.apnum.2021.05.006
Publikováno v:
Fractional Calculus and Applied Analysis. 24:1231-1256
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::15b4f339af21927f26ca950a875dac83
https://doi.org/10.1515/fca-2021-0053
https://doi.org/10.1515/fca-2021-0053
Publikováno v:
Computational Mathematics and Mathematical Physics. 61:1075-1093
The first boundary value problem for the fractional-order convection–diffusion equation is studied. A locally one-dimensional difference scheme is constructed. Using the maximum principle, a prior estimate is obtained in the uniform metric. The sta
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::da350e19721580491f8b779d14db8428
https://doi.org/10.1134/s0965542521070022
https://doi.org/10.1134/s0965542521070022
Autor:
Anatoly Alievich Alikhanov
Publikováno v:
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, Vol 17, Iss 1, Pp 15-23 (2013)
The Steklov nonlocal boundary value problem of the second kind for the simplest equations of mathematical physics is studied. A priori estimates for the solutions of the considered problems are obtained by using the method of energy inequalities. Uni
Externí odkaz:
https://doaj.org/article/42e3e9dee7194ab9875b846229438c1a
Publikováno v:
Computers & Mathematics with Applications. 79:2952-2972
A special point on each time interval is found for the approximation of the variable-order time Caputo derivative, which makes at least second order approximation accuracy be obtained. On this basis, two difference schemes are proposed for the multi-
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::73cf0100121eff12b0c958edddcef5b4
https://doi.org/10.1016/j.camwa.2020.01.003
https://doi.org/10.1016/j.camwa.2020.01.003
Publikováno v:
Computational Science – ICCS 2022 ISBN: 9783031087530
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7f41f30e787adae065e894a87be42a78
https://doi.org/10.1007/978-3-031-08754-7_8
https://doi.org/10.1007/978-3-031-08754-7_8
Autor:
Anatoly A. Alikhanov, Chengming Huang
Publikováno v:
Journal of Computational and Applied Mathematics. 414:114424
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::90947977ddc19d4b1846f23e31ca1432
https://doi.org/10.1016/j.cam.2022.114424
https://doi.org/10.1016/j.cam.2022.114424
Autor:
Chengming Huang, Anatoly A. Alikhanov
The present paper is devoted to constructing L2 type difference analog of the Caputo fractional derivative. The fundamental features of this difference operator are studied and it is used to construct difference schemes generating approximations of t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::80cecd710c4bbd5b72625cecdd892efb