For any n×n matrix A , we use the joint higher rank numerical range, Λk(A, . . . ,Am) , to define the higher rank numerical hull of A . We characterize the higher rank numerical hulls of Hermitian matrices. Also, the higher rank numerical hulls of unitary matrices are studied. Mathematics subject classification (2010): 15A60,81P68.

In this article the numerical approximation of solutions of Itô stochastic differential equations is considered, in particular for equations with a small parameter 2 in the noise coefficient. We construct stochastic linear multi-step methods and develop the fundamental numerical analysis concerning their mean-square consistency, numerical stability in the mean-square sense and mean-square conve...

The wave diffraction from a box in a two-layer fluid was studied by time-domain approach. The Rankine source is used in the upper layer to establish the boundary equation. While the Rankine source and its images are adopted in the lower fluid. Through the construction of a function by velocity potentials of upper and lower velocity potentials on the internal surface, a single set of linear equa...

The advent of supercomputers with hierarchical memory systems has imposed the use of block algorithms for the linear algebra algorithms. Although block algorithms may result in impressive improvements in performance, their numerical properties are quite different from their scalar counterpart and deserve an in-depth study. In this paper, the numerical stability ofblock Gram-Schmidt orthogonaliz...

Several algorithms have been proposed in the literature for the computation of the zeros of a linear system described by a state-space model 1x1 A,B,C,D}. In this report we discuss the numerical properties of a new algorithm and compare it with some earlier techniques of computing zeros. The new approach is shown to handle both nonsquare and/or degenerate systems without difficulties whereas ea...

An analysis has been performed to study the natural convection of a non-Newtonian fluid between two infinite parallel vertical flat plates and the effects of the non-Newtonian nature of fluid on the heat transfer are studied. The governing boundary layer and temperature equations for this problem are reduced to an ordinary form and are solved by Homotopy perturbation method (HPM) and numerical ...

The numerical methods in the current known literature require the stochastic differential equations SDEs driven by Poisson randommeasure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler’s method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. Themain aim...

in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...

The need to differentiate between epistemic and aleatory uncertainty is now well admitted by the risk analysis community. One way to do so is to model aleatory uncertainty by classical probability distributions and epistemic uncertainty by means of possibility distributions, and then propagate them by their respective calculus. The result of this propagation is a random fuzzy variable. When dea...

A linear program has a unique least 2-norm solution provided that the linear program has a solution. To locate this solution, most of the existing methods were devised to solve certain equivalent perturbed quadratic programs or unconstrained minimization problems. Different from these traditional methods, we provide in this paper a new theory and an effective numerical method to seek the least ...