2019/01/01 by Raimondas Čiegis, Ciegis, Raimondas, Petr Vabishchevich +1
Mathematics · #26A33 #35R11 #65F60 #65M06 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1901.00201
openalex publication_date 2019/01/01 · openalex created_date 2022/07/31 · openalex updated_date 2026/07/28
In many recent applications when new materials and technologies are developed\nit is important to describe and simulate new nonlinear and nonlocal diffusion\ntransport processes. A general class of such models deals with nonlocal\nfractional power elliptic operators. In order to solve these problems\nnumerically it is proposed (Petr N. Vabishchevich, Journal of Computational\nPhysics. 2015, Vol. 282, No.1, pp.289--302) to consider equivalent local\nnonstationary initial value pseudo-parabolic problems. Previously such problems\nwere solved by using the standard implicit backward and symmetrical Euler\nmethods. In this paper we use the one-parameter family of three-level finite\ndifference schemes for solving the initial value problem for the first order\nnonstationary pseudo-parabolic problem. The fourth-order approximation scheme\nis developed by selecting the optimal value of the weight parameter. The\nresults of the theoretical analysis are supplemented by results of extensive\ncomputational experiments.\n