We investigate the strong stability preserving (SSP) property of two-step Runge– Kutta (TSRK) methods. We prove that all SSP TSRK methods belong to a particularly simple subclass of TSRK methods, in which stages from the previous step are not used. We derive simple order conditions for this subclass. Whereas explicit SSP Runge–Kutta methods have order at most four, we prove that explicit SSP TS...

Determining the best initial parameter values for an algorithm, called parameter tuning, is crucial to obtaining better algorithm performance; however, it is often a time-consuming task and needs to be performed under a restricted computational budget. In this study, the results from our previous work on using the Taguchi method to tune the parameters of a memetic algorithm for cross-domain sea...

This note focuses on developing quasi-Newton methods that combine m+ 1 multistep and single-step updates on a single iteration for the sake of constructing the new approximation to the Hessian matrix to be used on the next iteration in computing the search direction. The approach considered here exploits the merits of the multistepmethods and those of El-Baali (1999) to create a hybrid techniqu...

The second order Ordinary Differential Equation (ODE) system obtained after semidiscretizing the wavetype Partial Differential Equation (PDE) with the Finite Element Method (FEM), shows strong numerical stiffness. Although it can be integrated using Matlab ode-solvers, the function ode15s offered by Matlab for solving stiff ODE systems does not result very efficient as its resolution requires t...

Interval methods for solving problems in differential equations and their implementation in floating-point interval arithmetic are interesting due to interval-solutions obtained which contain not only the errors of methods, but also all possible numerical errors. Such methods have been analyzed in a number of papers and monographs (see e.g. [1], [5], [9], and [10]). In our previous papers expli...

For solving hyperbolic systems with stiff sources or relaxation terms, time stepping methods should combine favorable monotonicity properties for shocks and steep solution gradients with good stability properties for stiff terms. In this paper we consider implicit–explicit (IMEX) multistep methods. Suitable methods will be constructed, based on explicit methods with general monotonicity and bou...

In this paper, we consider the asymptotic stability of linear constant coefficient delay differential-algebraic equations and of &methods, Runge-Kutta methods and linear multistep methods applied to these systems. o 1997 Published by Elsevier Science B.V.

Implicit–explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave–slow-wave problems in which the fast wave has relatively low amplitude and need not be accurately simulated. The widely used combination of trapezoidal implicit and leapfrog explicit differencing is compared to schemes based on Adams methods or on backward differenci...