A new class of homotopy continuation methods is developed suitable for globalizing quasiNewton methods for large sparse nonlinear systems of equations. The new continuation methods, described as monolithic homotopy continuation, differ from the classical predictor-corrector algorithm in that the predictor and corrector phases are replaced with a single phase which includes both a predictor and ...

Abstract This paper considers a new version of the discontinuous particle method, whose higher accuracy is based on “predictor-corrector” scheme. The peculiarity this criterion rearranging particles at “corrector” stage. In contrast to previously used with analysis overlapping particles, which required an assumption about their form, we use another key characteristic namely, mass, more precisel...

In this article, we consider the iterated Runge–Kutta (IRK) method which is an iteration method based on a predictor–corrector scheme for the solution of ordinary differential equations. The method uses embedded formulae to control the stepsize. We present different algorithms of the IRK method on distributed memory multiprocessors using appropriate communication primitives. The theoretical per...

In this paper, we consider some aspects of the numerical analysis mathematical model fractional Duffing with a derivative variable order Riemann-Liouville type. Using methods: an explicit finite-difference scheme based on Grunwald-Letnikov and Adams-Bashford-Moulton approximations (predictor-corrector), proposed is found. These methods have been verified test case. It shown that predictor-corre...

An interior point method (IPM) defines a search direction at each interior point of a region. These search directions form a direction field which in turn gives rise to a system of ordinary differential equations (ODEs). The solutions of the system of ODEs can be viewed as underlying paths in the interior of the region. In [C.-K. Sim and G. Zhao, Math. Program. Ser. A, 110 (2007), pp. 475–499],...

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...