An infinite family of one step iterators for solving non linear equation to increase the order of convergence and a new algoritm of global convergence

In this paper we present an infinite family of one-step iterative formulas for solving nonlinear equations (Present Method One), from now on PMI, that can be expressed as xn+1=Fm(xn), with 1=1, we will prove that the corresponding iteration formula of the family, xn+1= Fm0(xn), has an order of convergence m0+1. The increment of the velocity of convergence of the sequence of the iterator family xn+1=Fm+1(xn) with respect to the previous one xn+1=Fm(xn) is attained at the expense of one derivative evaluation more. Besides, we introduce a new algorithm (Present Method Two), from now on PMII, that plays the role of seeker for an initial value to guarantee the local convergence of the PMI. Both of them can be combined as an algorithm of global convergence, included the case of singular roots, that does not depend on the chosen initial value, and that allows to find all the roots in a feasible interval in a general and complete way. These are, in my opinion, the main results of this work. © 2013 Elsevier Ltd. All rights reserved.Moreno Flores, J. (2013). An infinite family of one step iterators for solving non linear equation to increase the order of convergence and a new algoritm of global convergence. Computers and Mathematics with Applications. 66(8):1418-1436. doi:10.1016/j.camwa.2013.08.003S1418143666

Effect of Random Parameter Switching on Commensurate Fractional Order Chaotic Systems

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.The paper explores the effect of random parameter switching in a fractional order (FO) unified chaotic system which captures the dynamics of three popular sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors. The disappearance of chaos in such systems which rapidly switch from one family to the other has been investigated here for the commensurate FO scenario. Our simulation study show that a noise-like random variation in the key parameter of the unified chaotic system along with a gradual decrease in the commensurate FO is capable of suppressing the chaotic fluctuations much earlier than that with the fixed parameter one. The chaotic time series produced by such random parameter switching in nonlinear dynamical systems have been characterized using the largest Lyapunov exponent (LLE) and Shannon entropy. The effect of choosing different simulation techniques for random parameter FO switched chaotic systems have also been explored through two frequency domain and three time domain methods. Such a noise-like random switching mechanism could be useful for stabilization and control of chaotic oscillation in many real-world applications

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

A framework for developing finite element codes for multi- disciplinary applications

The world of computing simulation has experienced great progresses in recent years and requires more exigent multidisciplinary challenges to satisfy the new upcoming demands. Increasing the importance of solving multi-disciplinary problems makes developers put more attention to these problems and deal with difficulties involved in developing software in this area. Conventional finite element codes have several difficulties in dealing with multi-disciplinary problems. Many of these codes are designed and implemented for solving a certain type of problems, generally involving a single field. Extending these codes to deal with another field of analysis usually consists of several problems and large amounts of modifications and implementations. Some typical difficulties are: predefined set of degrees of freedom per node, data structure with fixed set of defined variables, global list of variables for all entities, domain based interfaces, IO restriction in reading new data and writing new results and algorithm definition inside the code. A common approach is to connect different solvers via a master program which implements the interaction algorithms and also transfers data from one solver to another. This approach has been used successfully in practice but results duplicated implementation and redundant overhead of data storing and transferring which may be significant depending to the solvers data structure. The objective of this work is to design and implement a framework for building multi-disciplinary finite element programs. Generality, reusability, extendibility, good performance and memory efficiency are considered to be the main points in design and implementation of this framework. Preparing the structure for team development is another objective because usually a team of experts in different fields are involved in the development of multi-disciplinary code. Kratos, the framework created in this work, provides several tools for easy implementation of finite element applications and also provides a common platform for natural interaction of its applications in different ways. This is done not only by a number of innovations but also by collecting and reusing several existing works. In this work an innovative variable base interface is designed and implemented which is used at different levels of abstraction and showed to be very clear and extendible. Another innovation is a very efficient and flexible data structure which can be used to store any type of data in a type-safe manner. An extendible IO is also created to overcome another bottleneck in dealing with multi-disciplinary problems. Collecting different concepts of existing works and adapting them to coupled problems is considered to be another innovation in this work. Examples are using an interpreter, different data organizations and variable number of dofs per node. The kernel and application approach is used to reduce the possible conflicts arising between developers of different fields and layers are designed to reflect the working space of different developers also considering their programming knowledge. Finally several technical details are applied in order to increase the performance and efficiency of Kratos which makes it practically usable. This work is completed by demonstrating the framework’s functionality in practice. First some classical single field applications like thermal, fluid and structural applications are implemented and used as benchmark to prove its performance. These applications are used to solve coupled problems in order to demonstrate the natural interaction facility provided by the framework. Finally some less classical coupled finite element algorithms are implemented to show its high flexibility and extendibility

Solution of nonlinear dynamic structural systems by a hybrid frequency-time domain approach

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1983.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGBibliography: leaves 359-367.by James Daniel Kawamoto.Ph.D