This is a mathematical study of the long-lived hydromagnetic structures produced in the tenuous solar corona by the turbulent, resistive relaxation of a magnetic field under the condition of extremely high electrical conductivity. The relaxation theory of Taylor (1974), originally developed for a laboratory device, is extended to treat the open atmosphere where the relaxing field must interact ...

A method is shown that transforms the problem of inverting an ill-conditioned matrix to one of inverting a diagonally dominant matrix. An error analysis is outlined and the method is compared in theory and in result with the commonly used iterative methods. This direct method is demonstrated to be the limiting case of an nth-order iterative procedure as n approaches infinity. Examples are given...

It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C....

We first consider the size of problems that can currently be solved by sparse direct methods. We then discuss the limitations of such methods, where current research is going in moving these limitations, and how far we might expect to go with direct solvers in the near future. This leads us to the conclusion that very large systems, by which we mean three dimensional problems in more than a mil...

An interactive system for designing curved surfaces is proposed which is based on direct manipulation of a single-view shaded image of this surface. Apart from functions like carving in the surface or adding to it, and local smoothing, sharpening or shifting of selected surface regions, the system supports painting local gradient distributions. An iterative algorithm enforces conservativity of ...

The thesis of this paper is simple: that understanding both the construction and the interpretation of algebras is useful not only as a speciication technique for the implementation of interactive systems, but also as providing fundamental insights into the design and use of such systems in a general way. This is in contrast rstly to state-oriented speciication techniques like Z and VDM , which...

This paper provides a general framework for the quantitative estimation of the effects of removing negative features on engineering analysis, or modification sensitivity for short. There are two main applications: (i) when defeaturing models so that finite element analysis may be carried out more quickly and with lower memory requirements, and (ii) when performing iterative design based on fini...

This thesis presents a parallel resolution method for sparse linear systems which combines effectively techniques of direct and iterative solvers using a Schur complement approach. A domain decomposition is built ; the interiors of the subdomains are eliminated by a direct method in order to use an iterative method only on the interface unknowns. The system on the interface (Schur complement) i...

In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...