in general plane regions and with respect to linear boundary conditions, is a classical problem of numerical analysis. Many such boundary value problems have been solved successfully on high-speed computing machines, using the (iterative) Young-Frankel "successive overrelaxation" (SOR) method as defined in [l] and [2], and variants thereof ("line" and "block" overrelaxation). For this method, e...

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...

This research includes of the numerical modeling of fluids in two-dimensional cavity. The cavity flow is an important theoretical problem. In this research, modeling was carried out based on an alternating direction implicit via Vorticity-Stream function formulation. It evaluates different Reynolds numbers and grid sizes. Therefore, for the flow field analysis and prove of the ability of the sc...

This work introduces novel unconditionally stable operator splitting methods for solving the time dependent nonlinear Poisson-Boltzmann (NPB) equation for the electrostatic analysis of solvated biomolecules. In a pseudo-transient continuation solution of the NPB equation, a long time integration is needed to reach the steady state. This calls for time stepping schemes that are stable and accura...

We give a highly efficient, accurate and unconditionally stable algorithm to solve the partial differential equation for simulating the action potential propagation through cardiac tissue. In the new algorithm, we discretize the space domain by combining a compact finite difference scheme with an alternating direction implicit (ADI) scheme, which has fourth-order accuracy for interior mesh poin...

In this paper an analysis will be presented for the ADI (alternating direction implicit) method of Peaceman and Rachford applied to initial-boundary value problems for partial differential equations in two space dimensions. We shall use the method of lines approach. Motivated by developments in the field of stiff nonlinear ordinary differential equations, our analysis will focus on problems whe...

EEcient numerical schemes for nonlinear diiusion ltering based on additive operator splitting (AOS) were introduced in 15]. AOS schemes are eecient and unconditionally stable, yet their accuracy is limited. Future applications of nonlinear diiusion ltering may require better accuracy at the expense of a relatively modest cost in computations and complexity. In this report we explore second orde...

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...