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Generalized leapfrog methods. (English) Zbl 0637.65089
The generalized leap-frog methods, i.e. methods of the type \[ u_ m^{n+1}=\sum^{s}_{k=-r}a_ k(\mu)u\quad n_{m+k}+B(\mu)u^{n- 1}_{m+\quad L},\quad \mu =\Delta t/\Delta x \] for linear convective equations are considered. Here r and s are given constants, \(a_ k(\mu)\), b(\(\mu)\) and integer L are chosen. The questions of approximation, stability and behaviour of group velocity for such methods are discussed.
Reviewer: Yu.Shokin

MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L45 Initial value problems for first-order hyperbolic systems
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