We consider quadrature formulas of high order in time based on Radau–type, L–stable implicit Runge–Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs iterative deferred corrections to compute the solution at the collocation nodes of the quadrature formulas. The numerical stability is guaranteed by a dedic...

The Crank–Nicolson method can be used to solve the Black–Scholes partial differential equation in one-dimension when both accuracy and stability is of concern. In multi-dimensions, however, discretizing the computational grid with a Crank–Nicolson scheme requires significantly large storage compared to the widely adopted Operator Splitting Method (OSM). We found that symmetrizing the system of ...

Thispaper presents a method of simultaneous localization and mapping (SLAM) in indoor environment using extended Kalman filter (EKF) with the straight line segments as the adopted geometrical feature. By using conventional two dimensional laser range finder (LRF) as the main sensor, robot finds a number of points scanned from the surrounding environment.Split-and-Merge is one of the mostpopular...

We study the dual mixed finite element approximation of unilateral contact problems. Based on the dual mixed variational formulation with three unknowns (stress, displacement and the displacement on the contact boundary), the a priori error estimates have been established for both conforming and nonconforming finite element approximations. A Uzawa type iterative algorithm is developed to solve ...

Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...

Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...

We study some parallel overlapping Schwarz preconditioners for solving Stokeslike problems arising from finite element discretization of incompressible flow problems. Most of the existing methods are based on the splitting of the velocity and pressure variables. With the splitting, fast solution methods are often constructed using various fast Poisson solvers for one of the variables. More rece...

Abstract. In this paper we study the solution of singular integral equations by iterative methods. We show that discretization of singular integral operators obtained by domain splitting yields a system of algebraic equations that has a structure suitable for iterative solution. Numerical examples of Cauchy type singular integral equations are used to illustrate the proposed approach. This pape...