 A new simultaneously compact finite difference scheme for high-dimensional time-dependent PDEsReza Doostaki, Mohammad Mehdi Hosseini and Abbas Salemi Mathematics and Computers in Simulation (MATCOM), 2023, vol. 212, issue C, 504-523 Abstract: This paper presents a new compact finite difference scheme for solving linear high-dimensional time-dependent partial differential equations (PDEs). Despite the different spatial and time conditions in time-dependent problems, we propose a new compact finite difference scheme simultaneously both in time and space with arbitrary order accuracy. The merit of the proposed method is that the approximation of partial derivatives are derived simultaneously at all grid points. Also, by substituting the partial derivatives in the linear time-dependent PDEs a linear system of equations is derived. To show the efficiency and applicability of the proposed method, the fourth, sixth, and eighth-order simultaneously compact finite difference schemes are used for solving parabolic and convection–diffusion equations which have both time and spatial partial derivatives. The numerical results show the accuracy of the proposed method. Keywords: Compact finite difference scheme; Parabolic equations; Convection–diffusion equations; High-order accuracy (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:212:y:2023:i:c:p:504-523 DOI: 10.1016/j.matcom.2023.05.008 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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