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Implicit and semi-implicit schemes: Algorithms. (English) Zbl 0951.76059
From the summary: This study formulates general guidelines to extend an explicit code with a great variety of implicit and semi-implicit time integration schemes. The discussion is based on their specific implementation in the Versatile Advection Code, which is a general purpose software package for solving systems of nonlinear hyperbolic (and/or parabolic) partial differential equations, using standard high-resolution shock capturing schemes. For all combinations of explicit high resolution schemes with implicit and semi-implicit treatments, it is shown how second-order spatial and temporal accuracy for the smooth part of the solutions can be maintained. Strategies to obtain steady state and time accurate solutions implicitly are discussed.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics
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