in this paper, we design a new model of preconditioner for systems of linear equations. the convergence properties of the proposed methods have been analyzed and compared with the classical methods. numerical experiments of convection-diffusion equations show a good im- provement on the convergence, and show that the convergence rates of proposed methods are superior to the other modified itera...

in this paper, we present a comparative study between the modified variational iteration method (mvim) and a hybrid of fourier transform and variational iteration method (ftvim). the study outlines the efficiencyand convergence of the two methods. the analysis is illustrated by investigating four singular partial differential equations with variable coefficients. the solution of singular partia...

In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying...

Pamela Garcia Pulido , James Neal , Shawn Halpin , Khalid Hamandi * a Foundation Year 2, University Hospital of Wales, Cardiff CF14 4XW, United Kingdom Department of Neuropathology, University Hospital of Wales, Cardiff CF14 4XW, United Kingdom Department of Radiology, University Hospital of Wales, Cardiff CF14 4XW, United Kingdom d The Welsh Epilepsy Centre, University Hospital of Wales, Cardi...