Low-rank versions of the alternating direction implicit (ADI) iteration are popular and well established methods for the numerical solution of large-scale Sylvester and Lyapunov equations. Probably the largest disadvantage of these methods is their dependence on a set of shift parameters that are crucial for a fast convergence. Here we compare existing shifts generation strategies that compute ...

In this article, we investigate and analyze new methods for the numerical solution of three-dimensional nonlocal evolution problem arising in viscoelastic mechanics. Then these combine Galerkin finite element (FEMs) spatial discretization with corresponding alternating direction implicit (ADI) algorithms, based on backward Euler (BE) method Crank-Nicolson (CN) method, respectively, from which, ...

In this paper, a new algorithm for twodimensional (2-D) finite-difference time-domain (FDTD) method is presented. By this new method, the maximum time step size can be increased over the Courant-FriedrichLevy (CFL) condition restraint. This new algorithm is adapted from an Alternating-Direction Implicit FDTD (ADI-FDTD) method. However, unlike the ADI-FDTD algorithm, the alternation is performed...

In this paper, an unconditionally stable three-dimensional (3-D) finite-difference time-method (FDTD) is presented where the time step used is no longer restricted by stability but by accuracy. The principle of the alternating direction implicit (ADI) technique that has been used in formulating an unconditionally stable two-dimensional FDTD is applied. Unlike the conventional ADI algorithms, ho...

The alternating direction implicit (ADI) method is an attractive option to use in avoiding the CourantFriedrichs-Lewy (CFL) condition that limits the size of the time step required by explicit finite-difference time-domain (FDTD) methods for stability. Implicit methods like Crank-Nicholson offer the same advantages as ADI methods but they do not rely on simple, one-dimensional, tridiagonal syst...

For European plain vanilla options, we investigate the difference between solutions obtained by the full-scale and an approximate Heston-Hull-White (HHW) model. Based on the corresponding two option pricing PDEs, we analyze the quality of the approximation. To confirm the accuracy of the analysis, we solve the HHW PDE, its approximating PDE as well as the PDE for the error, numerically, via a s...

A numerical method is presented to solve a two-dimensional hyperbolic diffusion problem where is assumed that both convection and diffusion are responsible for flow motion. Since direct solutions based on implicit schemes for multidimensional problems are computa-tionally inefficient, we apply an alternating direction method which is second order accurate in time and space. The stability of the...

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence (CDI) FDTD method. In this paper, formulations from time-collocated to fundamental are presented ADI CDI methods. For implemented using E-E E-H update procedures, which comprise simple concise right-hand sides...

The Peaceman-Rachford alternating direction implicit (ADI) scheme for linear time-dependent Maxwell equations is analyzed on a heterogeneous cuboid. Due to discontinuities of the material parameters, solution less than H2-regular in space. For ADI scheme, we prove rigorous time-discrete error bound with convergence rate that half an order lower classical one. Our statement imposes only assumpti...