We present an extrapolative model of bubbles. In the model, many investors form their demand for a risky asset by weighing two signals—an average of the asset’s past price changes and the asset’s degree of overvaluation. The two signals are in conflict, and investors “waver” over time in the relative weight they put on them. The model predicts that good news about fundamentals can trigger large...

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...

We present a multilevel high order ADI method for separable generalized Helmholtz equations. The discretization method we use is a 1-D fourth order compact nite di erence applied to each directional component of the Laplace operator, resulting a discrete system e ciently solvable by ADI methods. We apply this high order di erence scheme to all levels of grids, and then starting from the coarses...

A new method is formulated and analyzed for the approximate solution of a twodimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the time-stepping, a novel alternating direction implicit (ADI) method based on the Crank-Nicolson method combined with the L1-approximation of the time Caputo derivative of...

In this paper we describe the 3-D Telegraph Equation (3-DTEL) with the use of Alternating Direction Implicit (ADI) method on Geranium Cadcam Cluster (GCC) with Message Passing Interface (MPI) parallel software. The algorithm is presented by the use of Single Program Multiple Data (SPMD) technique. The implementation is discussed by means of Parallel Design and Analysis with the use of Domain De...

The Poisson-Boltzmann (PB) model is an effective approach for the electrostatics analysis of solvated biomolecules. The nonlinearity associated with the PB equation is critical when the underlying electrostatic potential is strong, but is extremely difficult to solve numerically. In this paper, we construct two operator splitting alternating direction implicit (ADI) schemes to efficiently and s...

In this paper we propose a new projection method to solve large-scale continuous-time Lyapunov matrix equations. The new method projects the problem onto a much smaller approximation space, generated as a combination of Krylov subspaces in A and A. The reduced problem is then solved by means of a direct Lyapunov scheme based on matrix factorizations. The reported numerical results show the comp...

With a combined compact difference scheme for the spatial discretization and the CrankNicolson scheme for the temporal discretization, respectively, a high-order alternating direction implicit method (ADI) is proposed for solving unsteady two dimensional convectiondiffusion equations. The method is sixth-order accurate in space and second-order accurate in time. The resulting matrix at each ADI...

A novel Douglas alternating direction implicit (ADI) method is proposed in this work to solve a two-dimensional (2D) heat equation with interfaces. The ADI scheme is a powerful finite difference method for solving parabolic equations, due to its unconditional stability and high efficiency. However, it suffers from a serious accuracy reduction in space for interface problems with different mater...

Time domain simulations for high-frequency applications are widely dominated by the leapfrog timeintegration scheme. Especially in combination with the spatial discretization approach of the Finite Integration Technique (FIT) it leads to a highly efficient explicit simulation method, which in the special case of Cartesian grids can be regarded to be computationally equivalent to the Finite Diff...