Compact schemes in time with applications to partial differential equations

• Autor(a) principal: Clain, Stéphane
• Data de Publicação: 2023
• Outros Autores: Machado, Gaspar J., Malheiro, M. Teresa
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/1822/89115
• topic: Compact scheme; Structural equation; Time discretization; Very high-order; A-stability; Dispersion; Ciências Naturais::Matemáticas; Science & Technology

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, Schrodinger equation, wave equation, Burgers, and Euler system give the numerical evidences of the superior advantage of the method with respect to the traditional Runge-Kutta or multistep methods.