Download or read book Modern Solution Methods for Nonlinear Multidimensional Problems written by O.M. Belotserkovskii and published by . This book was released on 2000 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preparing the English translation the author has completely revised the Russian edition of 1994. The new versions and generalizations of computational algorithms which were intensively developed by the method of splitting with respect to physical processes are described.

Download or read book Modern Solution Methods for Nonlinear Multidimensional Problems written by O.M. Belotserkovskii and published by . This book was released on 2000 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preparing the English translation the author has completely revised the Russian edition of 1994. The new versions and generalizations of computational algorithms which were intensively developed by the method of splitting with respect to physical processes are described.

Download or read book Introduction to Multidimensional Integrable Equations written by B.G. Konopelchenko and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The soliton represents one ofthe most important ofnonlinear phenomena in modern physics. It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are found in various areas of physics from gravitation and field theory, plasma physics, and nonlinear optics to solid state physics and hydrodynamics. Nonlinear equations which describe soliton phenomena are ubiquitous. Solitons and the equations which commonly describe them are also of great mathematical interest. Thus, the dis covery in 1967and subsequent development ofthe inversescattering transform method that provides the mathematical structure underlying soliton theory constitutes one of the most important developments in modern theoretical physics. The inversescattering transform method is now established as a very powerful tool in the investigation of nonlinear partial differential equations. The inverse scattering transform method, since its discoverysome two decades ago, has been applied to a great variety of nonlinear equations which arise in diverse fields of physics. These include ordinary differential equations, partial differential equations, integrodifferential, and differential-difference equations. The inverse scattering trans form method has allowed the investigation of these equations in a manner comparable to that of the Fourier method for linear equations.

Download or read book Constructive Modeling of Structural Turbulence and Hydrodynamic Instabilities written by Oleg Mikha?lovich Belot?serkovski? and published by World Scientific. This book was released on 2009 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an original approach in the research of structural analysis of free developed shear compressible turbulence at high Reynolds number on the base of direct numerical simulation (DNS) and instability evolution for ideal medium (integral conservation laws) with approximate mechanism of dissipation (FLUX dissipative monotone ?upwind? difference schemes) and does not use any explicit sub-grid approximation and semi-empirical models of turbulence. Convective mixing is considered as a principal part of conservation law.Appropriate hydrodynamic instabilities (free developed shear turbulence) are investigated from unique point of view. It is based on the concept of large ordered structures with stochastic core of small scale developed turbulence (?turbulent spot?). Decay of ?turbulent spot? are simulated by Monte Carlo method. Proposed approach is based on two hypotheses: statistical independence of the characteristic of large ordered structures (LOS) and small-scale turbulence (ST) ?and? weak influence of molecular viscosity (or more generally, dissipative mechanism) on properties of large ordered structures.Two versions of instabilities, due to Rayleigh-Taylor and Richtmyer-Meshkov are studied detail by the three-dimensional calculations, extended to the large temporal intervals, up to turbulent stage and investigation turbulent mixing zone (TMZ).The book covers both the fundamental and practical aspects of turbulence and instability and summarizes the result of numerical experiments conducted over 30 years period with direct participation of the author.In the book are cited the opinions of the leading scientists in this area of research: Acad. A S Monin (Russia), Prof. Y Nakamura (Japan, Nagoya University) and Prof. F Harlow (USA, Los-Alamos).

Download or read book Group Theoretical Methods for Solving Multidimensional Nonlinear Partial Differential Equations written by Marianna Euler and published by . This book was released on 1998 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Innovative Methods for Numerical Solutions of Partial Differential Equations written by P. L. Roe and published by World Scientific. This book was released on 2002 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of 20 review articles dedicated to Prof. Philip Roe on the occasion of his 60th birthday and in appreciation of his original contributions to computational fluid dynamics. The articles, written by leading researchers in the field, cover many topics, including theory and applications, algorithm developments and modern computational techniques for industry. Contents: OC A One-Sided ViewOCO: The Real Story (B van Leer); Collocated Upwind Schemes for Ideal MHD (K G Powell); The Penultimate Scheme for Systems of Conservation Laws: Finite Difference ENO with Marquina's Flux Splitting (R P Fedkiw et al.); A Finite Element Based Level-Set Method for Multiphase Flows (B Engquist & A-K Tornberg); The GHOST Fluid Method for Viscous Flows (R P Fedkiw & X-D Liu); Factorizable Schemes for the Equations of Fluid Flow (D Sidilkover); Evolution Galerkin Methods as Finite Difference Schemes (K W Morton); Fluctuation Distribution Schemes on Adjustable Meshes for Scalar Hyperbolic Equations (M J Baines); Superconvergent Lift Estimates Through Adjoint Error Analysis (M B Giles & N A Pierce); Somewhere between the LaxOCoWendroff and Roe Schemes for Calculating Multidimensional Compressible Flows (A Lerat et al.); Flux Schemes for Solving Nonlinear Systems of Conservation Laws (J M Ghidaglia); A LaxOCoWendroff Type Theorem for Residual Schemes (R Abgrall et al.); Kinetic Schemes for Solving SaintOCoVenant Equations on Unstructured Grids (M O Bristeau & B Perthame); Nonlinear Projection Methods for Multi-Entropies NavierOCoStokes Systems (C Berthon & F Coquel); A Hybrid Fluctuation Splitting Scheme for Two-Dimensional Compressible Steady Flows (P De Palma et al.); Some Recent Developments in Kinetic Schemes Based on Least Squares and Entropy Variables (S M Deshpande); Difference Approximation for Scalar Conservation Law. Consistency with Entropy Condition from the Viewpoint of Oleinik's E-Condition (H Aiso); Lessons Learned from the Blast Wave Computation Using Overset Moving Grids: Grid Motion Improves the Resolution (K Fujii). Readership: Researchers and graduate students in numerical and computational mathematics in engineering."

Download or read book Innovations in Wave Processes Modelling and Decision Making written by Alena V. Favorskaya and published by Springer. This book was released on 2018-02-16 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods for full-wave computer simulation that can be used in various applications and contexts, e.g. seismic prospecting, earthquake stability, global seismic patterns on Earth and Mars, medicine, traumatology, ultrasound investigation of the human body, ultrasound and laser operations, ultrasonic non-destructive railway testing, modelling aircraft composites, modelling composite material delamination, etc. The key innovation of this approach is the ability to study spatial dynamical wave processes, which is made possible by cutting-edge numerical finite-difference grid-characteristic methods. The book will benefit all students, researchers, practitioners and professors interested in numerical mathematics, computer science, computer simulation, high-performance computer systems, unstructured meshes, interpolation, seismic prospecting, geophysics, medicine, non-destructive testing and composite materials.

Download or read book Parallel Computational Fluid Dynamics 2003 written by Boris Chetverushkin and published by Elsevier. This book was released on 2004-05-06 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to using of parallel multiprocessor computer systems for numerical simulation of the problems which can be described by the equations of continuum mechanics. Parallel algorithms and software, the problems of meta-computing are discussed in details, some results of high performance simulation of modern gas dynamic problems, combustion phenomena, plasma physics etc are presented. · Parallel Algorithms for Multidisciplinary Studies

Download or read book Methods in Nonlinear Analysis written by Kung Ching Chang and published by Springer. This book was released on 2009-09-02 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.

Download or read book Multipoint Methods for Solving Nonlinear Equations written by Miodrag Petkovic and published by Academic Press. This book was released on 2012-12-31 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoint methods have an extensive range of practical applications significant in research areas such as signal processing, analysis of convergence rate, fluid mechanics, solid state physics, and many others. The book takes an introductory approach in making qualitative comparisons of different multipoint methods from various viewpoints to help the reader understand applications of more complex methods. Evaluations are made to determine and predict efficiency and accuracy of presented models useful to wide a range of research areas along with many numerical examples for a deep understanding of the usefulness of each method. This book will make it possible for the researchers to tackle difficult problems and deepen their understanding of problem solving using numerical methods. Multipoint methods are of great practical importance, as they determine sequences of successive approximations for evaluative purposes. This is especially helpful in achieving the highest computational efficiency. The rapid development of digital computers and advanced computer arithmetic have provided a need for new methods useful to solving practical problems in a multitude of disciplines such as applied mathematics, computer science, engineering, physics, financial mathematics, and biology. Provides a succinct way of implementing a wide range of useful and important numerical algorithms for solving research problems Illustrates how numerical methods can be used to study problems which have applications in engineering and sciences, including signal processing, and control theory, and financial computation Facilitates a deeper insight into the development of methods, numerical analysis of convergence rate, and very detailed analysis of computational efficiency Provides a powerful means of learning by systematic experimentation with some of the many fascinating problems in science Includes highly efficient algorithms convenient for the implementation into the most common computer algebra systems such as Mathematica, MatLab, and Maple

Download or read book Computational Methods In Nonlinear Analysis Efficient Algorithms Fixed Point Theory And Applications written by Ioannis K Argyros and published by World Scientific. This book was released on 2013-07-11 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of computational sciences has seen a considerable development in mathematics, engineering sciences, and economic equilibrium theory. Researchers in this field are faced with the problem of solving a variety of equations or variational inequalities. We note that in computational sciences, the practice of numerical analysis for finding such solutions is essentially connected to variants of Newton's method. The efficient computational methods for finding the solutions of fixed point problems, nonlinear equations and variational inclusions are the first goal of the present book. The second goal is the applications of these methods in nonlinear problems and the connection with fixed point theory.This book is intended for researchers in computational sciences, and as a reference book for an advanced computational methods in nonlinear analysis. We collect the recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces, and present several applications and connections with fixed point theory. The book contains abundant and updated bibliography, and provides comparison between various investigations made in recent years in the field of computational nonlinear analysis.

Download or read book Lie and non Lie Symmetries Theory and Applications for Solving Nonlinear Models written by Roman M. Cherniha and published by MDPI. This book was released on 2018-07-06 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry

Download or read book Nonlinear Problems Present and Future written by A. Bishop and published by Elsevier. This book was released on 1982-01-01 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Problems: Present and Future

Download or read book Max Plus Methods for Nonlinear Control and Estimation written by William M. McEneaney and published by Springer Science & Business Media. This book was released on 2006 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. The max-plus-based methods examined in this work belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated Hamilton–Jacobi–Bellman (HJB) PDEs; these methods are not equivalent to either of the more commonly used finite element or characteristic approaches. Max-Plus Methods for Nonlinear Control and Estimation will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods.

Download or read book Problems of Nonlinear Deformation written by E.I. Grigolyuk and published by Springer Science & Business Media. This book was released on 1991-09-30 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in nonlinear problems in mechanics has been revived and intensified by the capacity of digital computers. Consequently, a question offundamental importance is the development of solution procedures which can be applied to a large class of problems. Nonlinear problems with a parameter constitute one such class. An important aspect of these problems is, as a rule, a question of the variation of the solution when the parameter is varied. Hence, the method of continuing the solution with respect to a parameter is a natural and, to a certain degree, universal tool for analysis. This book includes details of practical problems and the results of applying this method to a certain class of nonlinear problems in the field of deformable solid mechanics. In the Introduction, two forms of the method are presented, namely continu ous continuation, based on the integration of a Cauchy problem with respect to a parameter using explicit schemes, and discrete continuation, implementing step wise processes with respect to a parameter with the iterative improvement of the solution at each step. Difficulties which arise in continuing the solution in the neighbourhood of singular points are discussed and the problem of choosing the continuation parameter is formulated.

Download or read book The Numerical Solution of Nonlinear Problems written by Christopher T. H. Baker and published by Oxford University Press, USA. This book was released on 1981 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Methods in Nonlinear Analysis written by Kung Ching Chang and published by Springer Science & Business Media. This book was released on 2005-08-26 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.