The cooperative solution concept introduced here, the Stable Demand Set, contains the Core and is included in the Zhou Bargaining Set, eliminating the “dominated” coalition structures. The demand vectors belonging to the Stable Demand Set are self-stable. In the class of constant-sum homogeneous weighted majority games the Stable Demand Set is non-empty and predicts a unique stable demand vecto...

A fourth-order compact nite diierence scheme is employed with the multigrid algorithm to obtain highly accurate numerical solution of the convection-diiusion equation with very high Reynolds number and variable coeecients. The multigrid solution process is accelerated by a minimal residual smoothing (MRS) technique. Numerical experiments are employed to show that the proposed multigrid solver i...

A fourth-order compact nite diierence scheme is employed with the multigrid algorithm to obtain highly accurate numerical solution of the convection-diiusion equation with very high Reynolds number and variable coeecients. The multigrid solution process is accelerated by a minimal residual smoothing (MRS) technique. Numerical experiments are employed to show that the proposed multigrid solver i...

We investigate the basins of attraction of equilibrium points and minimal period-two solutions of the difference equation of the form x(n+1) = x²(n-1)/(ax²(n) + bx(n)x(n-1) + cx²(n-1)), n = 0,1, 2,…, where the parameters a,  b, and  c are positive numbers and the initial conditions x₋₁ and x₀ are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilib...

— We introduce small viscosity solutions of hyperbolic systems with discontinuous coefficients accross the fixed noncharacteristic hypersurface {xd = 0}. Under a geometric stability assumption, our first result is obtained, in the multi-D framework, for piecewise smooth coefficients. For our second result, the considered operator is ∂t+a(x)∂x, with sign(xa(x)) > 0 (expansive case not included i...

Multigrid preconditioners and solvers for the indefinite Helmholtz equation suffer from non-stability of the stationary smoothers due to the indefinite spectrum of the operator. In this paper we explore GMRES as a replacement for the stationary smoothers of the standard multigrid method. This results in a robust and efficient solver for a complex shifted or stretched Helmholtz problem that can ...