The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum ...

This paper presents a novel approach to recognize Grantha, an ancient script in South India and converting it to Malayalam, a prevalent language in South India using online character recognition mechanism. The motivation behind this work owes its credit to (i) developing a mechanism to recognize Grantha script in this modern world and (ii) affirming the strong connection among Grantha and Malay...

A new Peaceman–Rachford alternating direction implicit (PR-ADI) method is proposed in this work for solving two-dimensional (2D) parabolic interface problems with discontinuous solutions. The classical ADI schemes are known to be inaccurate for handling interfaces. This motivates the development of a matched Douglas ADI (D-ADI) method in the literature, in which the finite difference is locally...

An algorithm is presented for constructing an approximate numerical solution to a large scale Lyapunov equation in low rank factored form. The algorithm is based upon a synthesis of an approximate power method and an alternating direction implicit (ADI) method. The former is parameter free and tends to be efficient in practice, but there is little theoretical understanding of its convergence pr...

In this study, a numerical solution of 2D steady incompressible lid-driven cavity flow is presented. Three different numerical schemes were employed to make a comparison on the practicality of the methods. An alternating direction implicit scheme for the vorticity-stream function formulation, explicit and implicit schemes for the primitive variable formulation of governing Navier-Stokes equatio...

A Poisson-type equation arising in a commonly used numerical weather forecasting model is solved using an alternating direction implicit (ADI) method with Wachpress optimum parameters on a trapezoidal domain which coincides with the operational forecast domain. Various optimum parameter sequences were obtained for the corresponding squares which enclose the region under consideration, computati...

For large scale problems, an effective approach for solving the algebraic Lyapunov equation consists of projecting the problem onto a significantly smaller space and then solving the reduced order matrix equation. Although Krylov subspaces have been used for long time, only more recent developments have shown that rational Krylov subspaces can be a competitive alternative to the classical and v...

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...