An Extension of the Lax-Richtmyer Theory.
An extension of the perturbation analysis for the Drazin inverse.
An extension of the root perturbation -dimensional polynomial factorization method
An Extrapolation Method for the Quadrature of Functions with Singularities in the Vicinity of the Interval of Integration.
An Extrapolation Method with Step Size Control for Nonlinear Volterra Integral Equations.
An -Galerkin method for a Stefan problem with a quasilinear parabolic equation in nondivergence form.
An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...
An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...
An IMEX scheme for reaction-diffusion equations: application for a PEM fuel cell model
An implicit-explicit (IMEX) method is developed for the numerical solution of reaction-diffusion equations with pure Neumann boundary conditions. The corresponding method of lines scheme with finite differences is analyzed: explicit conditions are given for its convergence in the ‖·‖∞ norm. The results are applied to a model for determining the overpotential in a proton exchange membrane (PEM) fuel cell.
An immediate analysis for global superconvergence for integrodifferential equations
In this paper we study the finite element approximations to the parabolic and hyperbolic integrodifferential equations and present an immediate analysis for global superconvergence for these problems, without using the Ritz projection or its modified forms.
An imperfect conjugate gradient algorithm
A new biorthogonalization algorithm is defined which does not depend on the step-size used. The algorithm is suggested so as to minimize the total error after steps if imperfect steps are used. The majority of conjugate gradient algorithms are sensitive to the exactness of the line searches and this phenomenon may destroy the global efficiency of these algorithms.
An Implementation of Ray Tracing Algorithm for the Multiprocessor Machines
An implementation of recursive quadratic programming variable metric methods for linearly constrained nonlinear minimax approximation
An Implementation of the Method of Ermakov and Zolotukhin for Multidimensional Integration and Interpolation.
An Implementation of Vincent's Theorem.
An implicit approximate inverse preconditioner for saddle point problems.
An implicit iteration method for variational inequalities over the set of common fixed points for a finite family of nonexpansive mappings in Hilbert spaces.
An implicit method for fuzzy parabolic partial differential equations.
An implicit restarted Lanczos method for large symmetric eigenvalue problems.
An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...