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Title: | Compact schemes in time with applications to partial differential equations | Authors: | Clain, Stéphane Machado, Gaspar J. Malheiro, M.T. |
Keywords: | Compact scheme; Structural equation; Time discretization; Very high-order; A-stability Dispersion | Issue Date: | 2023 | Publisher: | Elsevier | Project: | UIDB/04650/2020 UIDB/00013/2020 UIDP/00013/2020 POCI-01-0145-FEDER-028118 PTDC/MAT-APL/28118/2017 |
Serial title, monograph or event: | Computers and Mathematics with Applications | Volume: | 140 | Abstract: | We propose a new class of fourth-and sixth-order schemes in time for parabolic and hyperbolic equations. The method follows the compact scheme methodology by elaborating implicit relations between the approximations of the function and its derivatives. We produce a series of A-stable methods with low dispersion and high accuracy. Several benchmarks for linear and non-linear Ordinary Differential Equations demonstrate the effectiveness of the method. Then a second set of numerical benchmarks for Partial Differential Equations such as convection-diffusion, Schrödinger equation, wave equation, Bürgers, and Euler system give the numerical evidences of the superior advantage of the method with respect to the traditional Runge-Kutta or multistep methods. | URI: | https://hdl.handle.net/10316/112372 | ISSN: | 08981221 | DOI: | 10.1016/j.camwa.2023.03.011 | Rights: | openAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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Compact schemes in time with applications to partial differential equations.pdf | 732.42 kB | Adobe PDF | View/Open |
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