When solving certain scalar transport problems, it is important to use fast methods that do not produce any parasitic oscillating solutions, but still have good energy conservation properties. The well known box scheme has these properties, but the use is restricted by severe conditions on the sign of the coefficients. In order to avoid this restriction, we introduce a modified method, that we call the shifted box scheme. It is very efficient for initial-boundary value problems, since it does not require more work per time step than an explicit scheme, while still being unconditionally stable.
Scalar transport problem box scheme initial-boundary value problem unconditional stability
This is a preview of subscription content, log in to check access
Hong Y., Liu J.L. (2004). Multisimplexity of centered box scheme for a class of Hamiltonian PDEs and an application to quasi-periodically solitary waves. Math. Comput. Modell. 39, 1035–1047CrossRefMATHMathSciNetADSGoogle Scholar
Keller H.B. (1971). A new difference scheme for parabolic problems. In: Hubbard B. (eds). Numerical solution of Partial Differential Equations, vol. 2, Academic, New York, pp. 327–350Google Scholar