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...

We develop certified tracking procedures for Newton homotopies, which are homotopies for which only the constant terms are changed. For these homotopies, our certified procedures include using a constant predictor with Newton corrections, an Euler predictor with no corrections, and an Euler predictor with Newton corrections. In each case, the predictor is guaranteed to produce a point in the qu...

How far the stability domain of a numerical method for approximating solutions to differential equations extends along the imaginary axis indicates how useful the method is for approximating solutions to wave equations; this maximum extent is termed the stability ordinate, also known as the imaginary stability boundary. It has previously been shown that exactly half of Adams-Bashforth, Adams-Mo...

Abstract Predictor–corrector schemes are designed to be a compromise retain the stability properties of implicit and computational efficiency explicit ones. In this paper complete analytical study for linear mean-square two-parameter family Euler predictor–corrector scalar stochastic differential equations is given. The analyzed given in terms two parameters that control degree implicitness met...

In this paper we discuss the polynomiality of Mehrotra-type predictor-corrector algorithms. We consider a variant of the original prototype of the algorithm that has been widely used in several IPM based optimization packages, for which no complexity result is known to date. By an example we show that in this variant the usual Mehrotra-type adaptive choice of the parameter μ might force the alg...

In this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (DTM). This is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. Several numerical examples are given and by comparing the numerical results obtained from DTM  and  predi...

An interior point method for monotone linear complementarity problems acting in a wide neighborhood of the central path is presented. The method has O( √ nL)iteration complexity and is superlinearly convergent even when the problem does not possess a strictly complementary solution.

Abstract We study a predictor-corrector interior-point algorithm for solving general linear complementarity problems from the implementation point of view. analyze method proposed by Illés, Nagy and Terlaky [1] that extends published Potra Liu [2] to problems. A new determining step size corrector direction is presented. Using code implemented in C++ programming language, we can solve large-sca...