Advances in Iterative Methods for Nonlinear Equations

Author: Sergio Amat,Sonia Busquier

Publisher: Springer

ISBN: 331939228X

Category: Mathematics

Page: 286

View: 1789

This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.

Advances in Numerical Analysis: Nonlinear partial differential equations and dynamical systems

Author: William Allan Light,Science and Engineering Research Council (Great Britain)

Publisher: Oxford University Press, USA

ISBN: 9780198534389

Category: Mathematics

Page: 288

View: 4726

The aim of this volume is to present research workers and graduate students in numerical analysis with a state-of-the-art survey of some of the most active areas of numerical analysis. This, and a companion volume, arise from a Summer School intended to cover recent trends in the subject. The chapters are written by the main lecturers at the School. Each is an internationally renowned expert in his respective field. This volume covers research in the numerical analysis of nonlinear phenomena: evolution equations, free boundary problems, spectral methods, and numerical methods for dynamical systems, nonlinear stability, and differential equations on manifolds.

Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer

Author: Ganji, Davood Domiri,Talarposhti, Roghayeh Abbasi

Publisher: IGI Global

ISBN: 1522527141

Category: Technology & Engineering

Page: 275

View: 1983

Engineering applications offer benefits and opportunities across a range of different industries and fields. By developing effective methods of analysis, results and solutions are produced with higher accuracy. Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer is an innovative source of academic research on the optimized techniques for analyzing heat transfer equations and the application of these methods across various fields. Highlighting pertinent topics such as the differential transformation method, industrial applications, and the homotopy perturbation method, this book is ideally designed for engineers, researchers, graduate students, professionals, and academics interested in applying new mathematical techniques in engineering sciences.

Recent Advances in Computational and Applied Mathematics

Author: Theodore E. Simos

Publisher: Springer Science & Business Media

ISBN: 9789048199815

Category: Mathematics

Page: 310

View: 3154

This multi-author contributed proceedings volume contains recent advances in several areas of Computational and Applied Mathematics. Each review is written by well known leaders of Computational and Applied Mathematics. The book gives a comprehensive account of a variety of topics including – Efficient Global Methods for the Numerical Solution of Nonlinear Systems of Two point Boundary Value Problems; Advances on collocation based numerical methods for Ordinary Differential Equations and Volterra Integral Equations; Basic Methods for Computing Special Functions, Melt Spinning: Optimal Control and Stability Issues; Brief survey on the CP methods for the Schrödinger equation; Symplectic Partitioned Runge-Kutta methods for the numerical integration of periodic and oscillatory problems. Recent Advances in Computational and Applied Mathematics is aimed at advanced undergraduates and researchers who are working in these fast moving fields.

Recent Advances in Numerical Methods and Applications II

Author: Oleg P Iliev,Mikhail S Kaschiev,Svetozar D Margenov,Blagovest H Sendov,Panayot S Vassilevski

Publisher: World Scientific

ISBN: 9814531855

Category:

Page: 924

View: 9498

This volume contains the proceedings of the 4th International Conference on Numerical Methods and Applications. The major topics covered include: general finite difference, finite volume, finite element and boundary element methods, general numerical linear algebra and parallel computations, numerical methods for nonlinear problems and multiscale methods, multigrid and domain decomposition methods, CFD computations, mathematical modeling in structural mechanics, and environmental and engineering applications. The volume reflects the current research trends in the specified areas of numerical methods and their applications. Contents: Computational Issues in Large Scale Eigenvalue ProblemsCombustion Modeling in Industrial FurnacesMonte Carlo MethodsMultilevel Methods for Incompressible Viscous FlowsApproximation of Nonlinear and Functional PDEsSolving Linear Systems with Error ControlRegular Numerical Methods for Inverse and Ill-Posed ProblemsMultifield ProblemsParallel and Distributed Numerical Computing with ApplicationsParameter-Robust Numerical Methods for Singularly Perturbed and Convection-Dominated ProblemsFinite Difference MethodsFinite Element MethodsFinite Volume MethodsBoundary Element MethodsNumerical Linear AlgebraNumerical Methods for Nonlinear ProblemsNumerical Methods for Multiscale ProblemsMultigrid and Domain DecompositionComputational Fluid DynamicsMathematical Modelling in Structural MechanicsEnvironmental ModellingEngineering Applications Readership: Researchers in applied mathematics and computational physics. Keywords:Numerical Methods and Applications;General Finite Difference;General Numerical Linear Algebra;Parallel Computations;Nonlinear Problems and Multiscale Methods

Projection methods for systems of equations

Author: Claude Brezinski

Publisher: North-Holland

ISBN: N.A

Category: Mathematics

Page: 400

View: 314

The solutions of systems of linear and nonlinear equations occurs in many situations and is therefore a question of major interest. Advances in computer technology has made it now possible to consider systems exceeding several hundred thousands of equations. However, there is a crucial need for more efficient algorithms. The main focus of this book (except the last chapter, which is devoted to systems of nonlinear equations) is the consideration of solving the problem of the linear equation Ax = b by an iterative method. Iterative methods for the solution of this question are described which are based on projections. Recently, such methods have received much attention from researchers in numerical linear algebra and have been applied to a wide range of problems. The book is intended for students and researchers in numerical analysis and for practitioners and engineers who require the most recent methods for solving their particular problem.

Numerical Methods for Differential Systems

Recent Developments in Algorithms, Software, and Applications

Author: L. Lapidus,W. E. Schiesser

Publisher: Elsevier

ISBN: 148326985X

Category: Mathematics

Page: 304

View: 1637

Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications reviews developments in algorithms, software, and applications of numerical methods for differential systems. Topics covered include numerical algorithms for ordinary and partial differential equations (ODE/PDEs); theoretical approaches to the solution of nonlinear algebraic and boundary value problems via associated differential systems; integration algorithms for initial-value ODEs with particular emphasis on stiff systems; finite difference algorithms; and general- and special-purpose computer codes for ODE/PDEs. Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework. Subsequent chapters focus on numerical methods for mass action kinetics; a systematized collection of codes for solving two-point boundary value problems; general software for PDEs; and the choice of algorithms in automated method of lines solution of PDEs. The final chapter is devoted to quality software for ODEs. This monograph should be of interest to mathematicians, chemists, and chemical engineers.

Advances in Numerical Simulation of Nonlinear Water Waves

Author: Qingwei Ma

Publisher: World Scientific

ISBN: 9812836500

Category: Mathematics

Page: 700

View: 7389

Most of the Earth''s surface is covered by water. Our everyday lives and activities are affected by water waves in oceans, such as the tsunami that occurred in the Indian Ocean on 26 December 2004. This indicates how important it is for us to fully understand water waves, in particular the very large ones. One way to do so is to perform numerical simulation based on the nonlinear theory. Considerable research advances have been made in this area over the past decade by developing various numerical methods and applying them to emerging problems; however, until now there has been no comprehensive book to reflect these advances. This unique volume aims to bridge this gap. This book contains 18 self-contained chapters written by more than 50 authors from 12 different countries, many of whom are world-leading experts in the field. Each chapter is based mainly on the pioneering work of the authors and their research teams over the past decades.The chapters altogether deal with almost all numerical methods that have so far been employed to simulate nonlinear water waves and cover many important and very interesting applications, such as overturning waves, breaking waves, waves generated by landslides, freak waves, solitary waves, tsunamis, sloshing waves, interaction of extreme waves with beaches, interaction with fixed structures, and interaction with free-response floating structures. Therefore, this book provides a comprehensive overview of the state-of-the-art research and key achievements in numerical modeling of nonlinear water waves, and serves as a unique reference for postgraduates, researchers and senior engineers working in industry.

Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis

Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Their Numerical Simulations

Author: Changpin Li,Yujiang Wu,Ruisong Ye

Publisher: World Scientific

ISBN: 981443647X

Category: Mathematics

Page: 416

View: 3555

Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation. Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed. In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc. In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications. Contents:Gronwall Inequalities (Fanhai Zeng, Jianxiong Cao and Changpin Li)Existence and Uniqueness of the Solutions to the Fractional Differential Equations (Yutian Ma, Fengrong Zhang and Changpin Li)Finite Element Methods for Fractional Differential Equations (Changpin Li and Fanhai Zeng)Fractional Step Method for the Nonlinear Conservation Laws with Fractional Dissipation (Can Li and Weihua Deng)Error Analysis of Spectral Method for the Space and Time Fractional Fokker–Planck Equation (Tinggang Zhao and Haiyan Xuan)A Discontinuous Finite Element Method for a Type of Fractional Cauchy Problem (Yunying Zheng)Asymptotic Analysis of a Singularly Perturbed Parabolic Problem in a General Smooth Domain (Yu-Jiang Wu, Na Zhang and Lun-Ji Song)Incremental Unknowns Methods for the ADI and ADSI Schemes (Ai-Li Yang, Yu-Jiang Wu and Zhong-Hua Yang)Stability of a Collocated FV Scheme for the 3D Navier–Stokes Equations (Xu Li and Shu-qin Wang)Computing the Multiple Positive Solutions to p–Henon Equation on the Unit Square (Zhaoxiang Li and Zhonghua Yang)Multilevel WBIUs Methods for Reaction–Diffusion Equations (Yang Wang, Yu-Jiang Wu and Ai-Li Yang)Models and Dynamics of Deterministically Growing Networks (Weigang Sun, Jingyuan Zhang and Guanrong Chen)On Different Approaches to Synchronization of Spatiotemporal Chaos in Complex Networks (Yuan Chai and Li-Qun Chen)Chaotic Dynamical Systems on Fractals and Their Applications to Image Encryption (Ruisong Ye, Yuru Zou and Jian Lu)Planar Crystallographic Symmetric Tiling Patterns Generated From Invariant Maps (Ruisong Ye, Haiying Zhao and Yuanlin Ma)Complex Dynamics in a Simple Two-Dimensional Discrete System (Huiqing Huang and Ruisong Ye)Approximate Periodic Solutions of Damped Harmonic Oscillators with Delayed Feedback (Qian Guo)The Numerical Methods in Option Pricing Problem (Xiong Bo)Synchronization and Its Control Between Two Coupled Networks (Yongqing Wu and Minghai Lü) Readership: Senior undergraduates, postgraduates and experts in nonlinear dynamics with numerical analysis. Keywords:Fractional Dynamics;Infinite Dimensional Dynamics;Network Dynamics;Fractal DynamicsKey Features:The topics in this edited book are very hot and highly impressiveIssues and methods of such topics in this edited book have not been made available yetThe present edited book is suitable for various levels of researchers, such as senior undergraduates, postgraduates, and experts

Control and Dynamic Systems V32: Advances in Aerospace Systems Dynamics and Control Systems Part 2 of 3

Advances in Theory and Applications

Author: C.T. Leonides

Publisher: Academic Press

ISBN: 0323162436

Category: Technology & Engineering

Page: 294

View: 8390

Control and Dynamic Systems: Advances in Theory in Applications, Volume 32: Advances in Aerospace Systems Dynamics and Control Systems, Part 2 of 3 deals with significant advances in technologies which support the development of aerospace systems. It also presents several algorithms and computational techniques used in complex aerospace systems. After discussing flight management systems (FMS), this volume presents techniques for treating complex aerospace systems models. These techniques include parameter identification, asymptotic perturbation method, reliability techniques, constrained optimization techniques, and computation methods for decoy discrimination and optimal targeting. This book is an excellent reference for research and professional workers in the field who want a comprehensive source of techniques with significant applied implications.

Advances in Neural Information Processing Systems 19

Proceedings of the 2006 Conference

Author: Bernhard Schölkopf,John Platt,Thomas Hofmann

Publisher: MIT Press

ISBN: 0262195682

Category: Computers

Page: 1643

View: 3710

The annual conference on NIPS is the flagship conference on neural computation. It draws top academic researchers from around the world & is considered to be a showcase conference for new developments in network algorithms & architectures. This volume contains all of the papers presented at NIPS 2006.

Numerical Methods for Hyperbolic and Kinetic Problems

CEMRACS 2003, Summer Research Center in Mathematics and Advances in Scientific Computing, July 21- August 29, 2003, CIRM, Marseille, France

Author: Stéphane Cordier

Publisher: European Mathematical Society

ISBN: 9783037190128

Category: Differential equations, Hyperbolic

Page: 359

View: 3837

Hyperbolic and kinetic equations arise in a large variety of industrial problems. For this reason, the Summer Mathematical Research Center on Scientific Computing and its Applications (CEMRACS), held at the Center of International Research in Mathematics (CIRM) in Luminy, was devoted to this topic. During a six-week period, junior and senior researchers worked full time on several projects proposed by industry and academia. Most of this work was completed later on, and the present book reflects these results. The articles address modelling issues as well as the development and comparisons of numerical methods in different situations. The applications include multi-phase flows, plasma physics, quantum particle dynamics, radiative transfer, sprays, and aeroacoustics. The text is aimed at researchers and engineers interested in applications arising from modelling and numerical simulation of hyperbolic and kinetic problems.

Advances in computer methods for partial differential equations-V

proceedings of the fifth IMACS International Symposium on Computer Methods for Partial Differential Equations, held at Lehigh University, Bethlehem, Pennsylvania, U.S.A., June 19-June 21, 1984

Author: International Association for Mathematics and Computers in Simulation,United States. Office of Naval Research

Publisher: N.A

ISBN: N.A

Category: Differential equations, Partial

Page: 558

View: 3992


A Contemporary Study of Iterative Methods

Convergence, Dynamics and Applications

Author: A. Alberto Magrenan,Ioannis Argyros

Publisher: Academic Press

ISBN: 0128094931

Category: Mathematics

Page: 400

View: 4652

A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand. Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography Explores the uses of computation of iterative methods across non-linear analysis Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options

Advances in Numerical Heat Transfer

Author: W. J. Minkowycz

Publisher: CRC Press

ISBN: 9781420095227

Category: Science

Page: 400

View: 4989

Definitive Treatment of the Numerical Simulation of Bioheat Transfer and Fluid Flow Motivated by the upwelling of current interest in subjects critical to human health, Advances in Numerical Heat Transfer, Volume 3 presents the latest information on bioheat and biofluid flow. Like its predecessors, this volume assembles a team of renowned international researchers who cover both fundamentals and applications. It explores ingenious modeling techniques and innovative numerical simulation for solving problems in biomedical engineering. The text begins with the modeling of thermal transport by perfusion within the framework of the porous-media theory. It goes on to review other perfusion models, different forms of the bioheat equation for several thermal therapies, and thermal transport in individual blood vessels. The book then describes thermal methods of tumor detection and treatment as well as issues of blood heating and cooling during lengthy surgeries. It also discusses how the enhancement of heat conduction in tumor tissue by intruded nanoparticles improves the efficacy of thermal destruction of the tumor. The final chapters focus on whole-body thermal models, issues concerning the thermal treatment of cancer, and a case study on the thermal ablation of an enlarged prostate.

Advances in Computational Mathematics

Author: Zhongying Chen,Yueshen Li,Charles Micchelli,Yuesheng Xu

Publisher: CRC Press

ISBN: 9780824719463

Category: Mathematics

Page: 632

View: 5180

This volume presents the refereed proceedings of the Guangzhou International Symposium on Computational Mathematics, held at the Zhongshan University, People's Republic of China. Nearly 90 international mathematicians examine numerical optimization methods, wavelet analysis, computational approximation, numerical solutions of differential and integral equations, numerical linear algebra, inverse and ill-posed problems, geometric modelling, and signal and image processing and their applications.