Abstract:
We consider linear schemes with several degrees of freedom (DOFs) for the transport equation with a constant coefficient. The Fourier transform decomposes the scheme into a number of finite systems of ODEs, the number of equations in each system being equal to the number of DOFs. The matrix of these systems is an analytical function of the wave vector. Generally such a matrix is not diagonalizable and, if it is, the diagonal form can be non-smooth. We show that in a 1D case for L2L2-stable schemes the matrix can be locally transformed to a block-diagonal form preserving the analytical dependence on the wave number.
This publication is cited in the following 2 articles:
P.A. Bakhvalov, M.D. Surnachev, “On the stability of finite-volume schemes on non-uniform meshes”, Mathematics and Computers in Simulation, 2025
Pavel Bakhvalov, Mikhail Surnachev, “Linear schemes with several degrees of freedom for the transport equation and the long-time simulation accuracy”, IMA Journal of Numerical Analysis, 44:1 (2024), 297