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...

The solution of an optimal power ow (OPF) problem in rectangular form by an interior-point method (IPM) for nonlinear programming is described. When formulated in rectangular form, some OPF variants have quadratic objective and quadratic constraints. Such quadratic features allow for ease of matrix setup and inexpensive incorporation of higher-order information in a predictor-corrector procedur...

It is well known that the so-called first-order predictor-corrector methods working in a large neighborhood of the central path are among the most efficient interior-point methods (IPMs) for linear optimization (LO) problems. However, the best known iteration complexity of this type of methods is O (

This paper considers the development of a two-point predictor-corrector block method for solving delay differential equations. The formulae are represented in divided difference form and the algorithm is implemented in variable stepsize variable order technique. The block method produces two new values at a single integration step. Numerical results are compared with existing methods and it is ...

The paper extends prior work by the authors on LOQO, an interior point algorithm for nonconvex nonlinear programming. The specific topics covered include primal versus dual orderings and higher order methods, which attempt to use each factorization of the Hessian matrix more than once to improve computational efficiency. Results show that unlike linear and convex quadratic programming, higher o...

We discuss a procedure for numerically approximating solutions to a system of nonlinear partial diierential equations which describe mountain pine beetles attacking lodgepole pine en masse. A centered spatial dicretization which yields a system of ordinary diierential equations is presented, including a method for generating`trans-parent' spatial boundary conditions. A ux-based model estimates ...

in this paper‎, ‎we propose a modification of the second order method‎ ‎introduced in [‎‎q. li and ‎x‎. ‎y. ‎wu‎, a two-step explicit $p$-stable method for solving second order initial value problems‎, ‎textit{‎appl‎. ‎math‎. ‎comput‎.}‎ {‎138}‎ (2003)‎, no. 2-3, ‎435--442‎] for the numerical solution of‎ ‎ivps for second order odes‎. ‎the numerical results obtained by the‎ ‎new method for some...

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...

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...