Abstract: In this paper, we present a class of multistep methods for the numerical solution of stiff ordinary differential equations. In these methods the first, second and third derivatives of the solution are used to improve the accuracy and absolute stability regions of the methods. The constructed methods are A-stable up to order 6 and A(α)-stable up to order 8 so that, as it is shown in th...

There have been interesting recent developments in methods for solving optimization problems without making use of derivative (sensitivity) information. While calculus based methods that employ derivative information can be extremely eecient and very eeec-tive, they are not applicable to all MDO problems, for instance, when the function to be optimized is nondiierentiable, when sensitivity info...

We propose feasible descent methods for constrained minimization that do not make explicit use of objective derivative information. The methods at each iteration sample the objective function value along a finite set of feasible search arcs and decrease the sampling stepsize if an improved objective function value is not sampled. The search arcs are obtained by projecting search direction rays ...

Following the work of Enright [3] there has been interest in studying second derivative methods for solving stiff ordinary differential equations. Successful implementations of second derivative methods have been reported by Enright [3], Sacks-Davis [9], [10] and Addison[l]. Wallace and Gupta [13] have suggested a polynomial formulation of the usual first-derivative multistep methods. Recently ...

Traditionally, syllogisms are arguments with two premises and one conclusion which are constructed by propositions of the form “All... are...” and “At least one... is...” and their respective negated versions. Unfortunately, the practical use of traditional syllogisms is quite restricted. On the one hand, the “All...” propositions are too strict, since a single counterexample suffices for falsi...

In this paper, we apply the local fractional Adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of Fredholm integral equations of the second kind within local fractional derivative operators. The iteration procedure is based on local fractional derivative. The obtained results reveal that the proposed methods are very efficient and simple tools ...

Abstract In this paper, mixed-integer nonsmooth constrained optimization problems are considered, where objective/constraint functions available only as the output of a black-box zeroth-order oracle that does not provide derivative information. A new derivative-free linesearch-based algorithmic framework is proposed to suitably handle those problems. First, scheme for bound combines dense seque...