no. 3
Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 3, pp. 845-878

This paper deals with the construction of a family of fourth order, energy consistent, explicit time discretizations for dissipative linear wave equations. The schemes are obtained by replacing the inversion of a matrix, that comes naturally after using the technique of the Modified Equation on the second order Leap Frog scheme applied to dissipative linear wave equations, by explicit approximations of its inverse. The stability of the schemes are studied using an energy analysis and a convergence analysis is carried out. Numerical results in 1D illustrate the space/time convergence properties of the schemes and their efficiency is compared to more classical time discretizations.

DOI : 10.1051/m2an/2019079
Classification : 00A71, 35L05, 85A20, 33C55, 65M60
Keywords: Dissipative linear wave equation, high order time discretisation, energy analysis 
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     author = {Chabassier, Juliette and Diaz, Julien and Imperiale, S\'ebastien},
     title = {Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {845--878},
     year = {2020},
     publisher = {EDP Sciences},
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Chabassier, Juliette; Diaz, Julien; Imperiale, Sébastien. Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 3, pp. 845-878. doi: 10.1051/m2an/2019079

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