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...

An infeasible start predictor-corrector algorithm for semideenite programming is proposed. It is a direct extension of the Mizuno-Todd-Ye predictor-corrector algorithm for linear programming. The algorithm uses the

This paper presents and evaluates the numerical solution of a coupled system of equations that arises in a model for the formation and evolution of three-dimensional longshore sand ridges. The model is based on the interaction between surrcial or internal weakly nonlinear shallow-water waves, having weak spanwise spatial dependence, and the deformable bottom topography. The presentation of the ...

In this paper, we present a predictor-corrector path-following interior-point algorithm for symmetric cone optimization based on Darvay's technique. Each iteration of the algorithm contains a predictor step and a corrector step based on a modification of the Nesterov and Todd directions. Moreover, we show that the algorithm is well defined and that the obtained iteration bound is √ log , where ...

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge–Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditi...

This paper investigates parallel predictor-corrector iteration schemes (PC iteration schemes) based on collocation Runge-Kutta corrector methods (RK corrector methods) with continuous output formulas for solving nonstiff initial-value problems (IVPs) for systems of first-order differential equations. The resulting parallel-iterated RK-type PC methods are also provided with continuous output for...

The higher order predictor (43) from [1] has to be modified in the degenerate case in order for the asymptotic convergence results from Lemma 4.6 and Theorem 4.7 to hold. More precisely equation (43) should be replaced by: where = 0 , if HLCP is nondegenerate 1 , if HLCP is degenerate. (2) The computational complexity results hold for the new algorithm, with slight modifications in the proof. C...

In this paper we present new numerical approach to solve the continuous casting problem. The main tool is to use IPEC method and DDM similar to Lapin and Pieska [2002] with multilevel domain decomposition. On the subdomains we use multidecomposition of the subdomains. The IPEC is used both in the whole calculation domain and inside the subdomains. The calculation algorithm is presented and nume...

A new voltage stability control model was presented to guarantee the static voltage stability of power system using the active power constraints of weak branches as the static voltage stability margin constraints. A local index for voltage stability was used to recognize the key contingencies, the weak branches and their maximum active power. Based on DC power flow equations, a static security ...

Adams-Bashforth-Moulton algorithm has been extended to solve delay differential equations of fractional order. Numerical illustrations are presented to demonstrate utility of the method. Chaotic behaviour is observed in one dimensional delayed systems of fractional order. We further find the smallest fractional order for the chaotic behaviour. It is also observed that the phase portraits get st...