An efficient, iterative semi-implicit (SI) numerical method for the time integration of stiff wave systems is presented. Physics-based assumptions are used to derive a convergent iterative formulation of the SI scheme which enables the monitoring and control of the error introduced by the SI operator. This iteration essentially turns a semi-implicit method into a fully implicit method. Accuracy...

We establish a rate of convergence for a semi-discrete operator splitting method applied to Hamilton-Jacobi equations with source terms. The method is based on sequentially solving a Hamilton-Jacobi equation and an ordinary diierential equation. The Hamilton-Jacobi equation is solved exactly while the ordinary diierential equation is solved exactly or by an explicit Euler method. We prove that ...

Under consideration is the following question. If T is a linear operator from a normed function space 3 into a Banach space X, then may an appropriate topology 3 be defined so that conditions on T may be interpreted in terms of the topology 3? For the present we consider 3 to be the class of Banach function spaces. We define appropriate "semi-norm topologies" on the unit ball x! of the dual of ...

The concept of K-quasi-hyponormal operators on semi-Hilbertian space is defined by Ould Ahmed Mahmoud Sid and Abdelkader Benali in [7]. This paper devoted to the study new class H, ∥. ∥Acalled (n,m)power-A-quasi-hyponormal denoted [(n,m)QH]A.We give some basic properties these examples are also given .An operator T ∈ BA(H) said be (n,m) power-A-quasi-hyponormal for positive A integers n m if T⋕...

Let £ be a partially ordered linear normed space over the field of real numbers whose positive cone K has nonempty interior K0.1 A functional / in E*, the conjugate space of E, is called positive if f(K)^0 and/5^0. A semi-group V of linear operators on E is called positive if r(A7) QK. It will be assumed that T contains the identity operator. This note is concerned with the properties of positi...

In this paper, we find explicit solution to the operator equation $TXS^* -SX^*T^*=A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $T,S$ have closed ranges and $S$ is a self adjoint operator.

1. Preliminaries. Only bounded operators on a Hilbert space § of elements x will be considered. If A is self-ad joint with the spectral resolution (1) A=f\dE(k), and if ^a = £>aC4) denotes the set of elements x for which ||E(X)#|| is an absolutely continuous function of X, then § 0 is a subspace; cf. [2, p. 240], [3, p. 436] and [6, p. 104]. If £ = £«, then A is called absolutely continuous. Th...

In the present work, we investigate the error behaviour of exponential operator splitting methods for nonlinear evolutionary problems of the form u ′(t) = A ( u(t) ) +B ( u(t) ) , 0≤ t ≤ T , u(0) given . In particular, our concern is to deduce an exact local error representation that is suitable in the presence of critical parameters. Essential tools in the theoretical analysis including time-d...