Numerical Algorithms

Abstract In this paper, we study a variation of the HSS Iteration method. This variation is based on a method introduced by Douglas and Rachford and has been called the Douglas-Rachford iterative method throughout the literature. A convergence criteria is given for positive definite matrices which is similar to the convergence criteria for the HSS iterative method. Examples are given to illustrat…

Abstract We define and analyze preconditioners for the Riesz operator $$-(- \Delta )^{\frac{\alpha }{2}}$$ , $$\alpha \in (1,2]$$ commonly used in fractional models, such as anomalous diffusion. For $$\alpha$$ close to 2 there are various effective preconditioners at disposal with linear computational cost. Seminal results on treatment of the case $$\alpha$$ near 1 that still maintains linear com…

This study presents and evaluates four distinct case studies concerning the transient (unsteady) heat conduction equation. The Meshless Local Petrov-Galerkin (MLPG) method is employed, and a direct comparison is performed between the distinct approximation functions: the Moving Least-Squares (MLS), the Radial Point Interpolation Method (RPIM) and the Interpolating Moving Least-Squares(IMLS). The …