We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka[4], for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding ...
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We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka[4], for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding line-wise versions. The resulting relaxation schemes are integrated into the multigrid solver based on second-order upwind differencing presented in [5]. Numerical comparisons on the efficiency of point-wise and line-wise relaxations are presented
The stability of symplectic algorithms is discussed in this paper. There are following conclusions. 1. Symplectic Runge-Kutta methods and symplectic one-step methods with high order derivative are unconditionally crit...
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The stability of symplectic algorithms is discussed in this paper. There are following conclusions. 1. Symplectic Runge-Kutta methods and symplectic one-step methods with high order derivative are unconditionally critically stable for Hamiltonian systems. Only some of them are A-stable for non-Hamiltonian systems. The criterion of judging A-stability is given. 2. The hopscotch schemes are conditionally critically stable for Hamiltonian systems. Their stability regions are only a segment on the imaginary axis for non-Hamiltonian systems. 3. All linear symplectic multistep methods are conditionally critically stable except the trapezoidal formula which is unconditionally critically stable for Hamiltonian systems. Only the trapezoidal formula is A-stable, and others only have segments on the imaginary axis as their stability regions for non-Hamiltonian systems.
The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme of q-th order, while the simplified order conditions for canonical RKN methods which...
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The main purpose of this paper is to develop and simplify the general conditions for an s-stage explicit canonical difference scheme of q-th order, while the simplified order conditions for canonical RKN methods which are applied to a special kind of second order ordinary differential equations are also obtained here.
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