In this paper, we give a new method for solving large scale problems. The basic idea of this method depends on implementing the conjugate gradient as a corrector into a continuation method. We use the Euler method as a predictor. Adaptive steplength control is used during the tracing of the solution curve. We present some of our experimental examples to demonstrate the efficiency of the method.

Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra...

The stability and convergence of fundamental numerical methods for solving ordinary differential equations are presented. These include one-step methods such as the classical Euler method, Runge–Kutta methods and the less well known but fast and accurate Taylor series method. We also consider the generalization to multistep methods such as Adams methods and their implementation as predictor–cor...

We present a new three-dimensional numerical model for the simulation of breaking waves. In proposed model, integral contravariant form Navier-Stokes equations is expressed in curvilinear moving coordinate system and are integrated by predictor-corrector method. predictor step method, motion discretized shock-capturing scheme that based on an original highorder reconstruction point values conse...

This paper presents an efticient technique for real-time tracking of a single moving object in terrestrial scenes using a stationary camera. The tracking algorithm is based on the Linear Prediction (LP) solved by the Maximum Entropy Method (MEM). It attempts to predict the centroid of the moving object in the next frame, based on several past centroid measurements. Using a second order of the L...

Applications in materials, medicine, and computers are being discovered where the control of events at the molecular and nanoscopic scales is critical to product quality, while the primary manipulation of these events during processing occurs at macroscopic length scales. In such applications, one of the most significant engineering challenges is to achieve control over phenomena that occur sim...

This paper discusses predictor-corrector iteration schemes (PC iteration schemes) based on direct collocation-based Runge-Kutta-Nystr??m corrector methods (RKN corrector methods) for solving nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y??(t)=f(y(t)). Our approach is to regard the well-known parallel-iterated RKN methods (PIRKN methods) as PC...

The smooth variable structure filter (SVSF) is a relatively new state and parameter estimation technique. Introduced in 2007, it is based on the sliding mode concept, and is formulated in a predictor-corrector fashion. The main advantages of the SVSF, over other estimation methods, are robustness to modeling errors and uncertainties, and its ability to detect system changes. Recent developments...