Three primal-dual interior-point algorithms for homogeneous cone programming are presented. They are a short-step algorithm, a large-update algorithm, and a predictor-corrector algorithm. These algorithms are described and analyzed based on a characterization of homogeneous cone via T -algebra. The analysis show that the algorithms have polynomial iteration complexity.

The Advanced Multilevel Predictor-Corrector Quasi-static Method (AML-PCQM) is proposed in this work. four computational levels, including transport, Multi-Group (MG) Coarse Mesh Finite Difference (CMFD), One-Group (1G) CMFD, and Exact Point-Kinetics Equation (EPKE), are coupled with a new dynamic iteration strategy. In each coupling algorithm, the original Transient Fixed Source Problem (TFSP) ...

A new, more accurate Hessian-based predictor-corrector algorithm has been developed for simulating classical trajectories of molecules in intense laser fields. The first and second derivatives of the gradient with respect to the electric field are included in the both the predictor and the corrector steps for integrating trajectories. A Taylor expansion of the gradient is used as the surface fo...

In this paper, a real-time reentry guidance law for hypersonic vehicles is presented to accomplish rapid, high-precision, robust, and reliable flights by leveraging the Time Vector (Time2vec) transformer networks. First, referring traditional predictor–corrector algorithm quasi-equilibrium glide condition (QEGC), issue described as univariate root-finding problem based on bank angle. Second, co...

in this paper, the (m+1)-step adams-bashforth, adams-moulton, and predictor-correctormethods are used to solve rst-order linear fuzzy ordinary dierential equations. the conceptsof fuzzy interpolation and generalised strongly dierentiability are used, to obtaingeneral algorithms. each of these algorithms has advantages over current methods. moreover,for each algorithm a convergence formula can b...

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 ...

The Constraint Consensus method moves quickly from an initial infeasible point to a point that is close to feasibility for a set of nonlinear constraints. It is a useful first step prior to launching an expensive local solver, improving the probability that the local solver will find a solution and the speed with which it is found. The two main ingredients are the method for calculating the fea...

This paper is devoted to the study of a new class of nonconvex variational inequalities, named general regularized nonconvex variational inequalities. By using the auxiliary principle technique, a new modified predictor–corrector iterative algorithm for solving general regularized nonconvex variational inequalities is suggested and analyzed. The convergence of the iterative algorithm is establi...

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...