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Homotopy Method For The Eigenvalue Problem For Partial Differential Equations
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Book Synopsis Homotopy Method for the Eigenvalue Problem for Partial Differential Equations by : Stanford University. Computer Science Department. Scientific Computing and Computational Mathematics Program
Download or read book Homotopy Method for the Eigenvalue Problem for Partial Differential Equations written by Stanford University. Computer Science Department. Scientific Computing and Computational Mathematics Program and published by . This book was released on 1994 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homotopy Analysis Method in Nonlinear Differential Equations by : Shijun Liao
Download or read book Homotopy Analysis Method in Nonlinear Differential Equations written by Shijun Liao and published by Springer Science & Business Media. This book was released on 2012-06-22 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.
Book Synopsis The Homotopy Method for the Symmetric Eigen-value Problems by : Noah H. Rhee
Download or read book The Homotopy Method for the Symmetric Eigen-value Problems written by Noah H. Rhee and published by . This book was released on 1987 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Krzysztof P. Rybakowski Publisher :Springer Science & Business Media ISBN 13 :3642728332 Total Pages :217 pages Book Rating :4.6/5 (427 download)
Book Synopsis The Homotopy Index and Partial Differential Equations by : Krzysztof P. Rybakowski
Download or read book The Homotopy Index and Partial Differential Equations written by Krzysztof P. Rybakowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: The homotopy index theory was developed by Charles Conley for two sided flows on compact spaces. The homotopy or Conley index, which provides an algebraic-topologi cal measure of an isolated invariant set, is defined to be the ho motopy type of the quotient space N /N , where is a certain 1 2 1 2 compact pair, called an index pair. Roughly speaking, N1 isolates the invariant set and N2 is the "exit ramp" of N . 1 It is shown that the index is independent of the choice of the in dex pair and is invariant under homotopic perturbations of the flow. Moreover, the homotopy index generalizes the Morse index of a nQnde generate critical point p with respect to a gradient flow on a com pact manifold. In fact if the Morse index of p is k, then the homo topy index of the invariant set {p} is Ik - the homotopy type of the pointed k-dimensional unit sphere.
Book Synopsis Beyond Perturbation by : Shijun Liao
Download or read book Beyond Perturbation written by Shijun Liao and published by CRC Press. This book was released on 2003-10-27 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, and even perturbation approximations are valid only for problems with weak nonlinearity. This book introduces a powerful new analytic method for nonlinear problems-homotopy analysis-that remains valid even with strong nonlinearity. In Part I, the author starts with a very simple example, then presents the basic ideas, detailed procedures, and the advantages (and limitations) of homotopy analysis. Part II illustrates the application of homotopy analysis to many interesting nonlinear problems. These range from simple bifurcations of a nonlinear boundary-value problem to the Thomas-Fermi atom model, Volterra's population model, Von Karman swirling viscous flow, and nonlinear progressive waves in deep water. Although the homotopy analysis method has been verified in a number of prestigious journals, it has yet to be fully detailed in book form. Written by a pioneer in its development, Beyond Pertubation: Introduction to the Homotopy Analysis Method is your first opportunity to explore the details of this valuable new approach, add it to your analytic toolbox, and perhaps make contributions to some of the questions that remain open.
Book Synopsis Advances In The Homotopy Analysis Method by : Shijun Liao
Download or read book Advances In The Homotopy Analysis Method written by Shijun Liao and published by World Scientific. This book was released on 2013-11-26 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the HAM from all other analytic approximation methods. In addition, the HAM can be applied to solve some challenging problems with high nonlinearity.This book, edited by the pioneer and founder of the HAM, describes the current advances of this powerful analytic approximation method for highly nonlinear problems. Coming from different countries and fields of research, the authors of each chapter are top experts in the HAM and its applications.
Book Synopsis The Optimal Homotopy Asymptotic Method by : Vasile Marinca
Download or read book The Optimal Homotopy Asymptotic Method written by Vasile Marinca and published by Springer. This book was released on 2015-04-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.
Book Synopsis Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by : Mitsuhiro T. Nakao
Download or read book Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations written by Mitsuhiro T. Nakao and published by Springer Nature. This book was released on 2019-11-11 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Calculus of Variations and Partial Differential Equations by : Luigi Ambrosio
Download or read book Calculus of Variations and Partial Differential Equations written by Luigi Ambrosio and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.
Book Synopsis Homotopy Methods for Nonlinear Partial Differential Equation Systems by : Wenrui Hao
Download or read book Homotopy Methods for Nonlinear Partial Differential Equation Systems written by Wenrui Hao and published by . This book was released on 2013 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homotopy-determinant Method for Solving Matrix Eigenvalue Problems and Its Parallelization by : Zhonggang Zeng
Download or read book Homotopy-determinant Method for Solving Matrix Eigenvalue Problems and Its Parallelization written by Zhonggang Zeng and published by . This book was released on 1991 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Study of Eigenvalue and Bifurcation Problems for Nonlinear Elliptic Partial Differential Equations Via Topological Continuation Methods by : Klaus Schmitt
Download or read book A Study of Eigenvalue and Bifurcation Problems for Nonlinear Elliptic Partial Differential Equations Via Topological Continuation Methods written by Klaus Schmitt and published by . This book was released on 1982 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variational Methods by : Michael Struwe
Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilberts talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.
Book Synopsis Advances in Numerical Partial Differential Equations and Optimization by : Susana Gomez
Download or read book Advances in Numerical Partial Differential Equations and Optimization written by Susana Gomez and published by SIAM. This book was released on 1990-12-31 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume emphasize the numerical aspects of three main areas: optimization, linear algebra and partial differential equations. Held in January, 1989, in Yucatan, Mexico, the workshop was organized by the Institute for Research in Applied Mathematics of the National University of Mexico in collaboration with the mathematical Sciences Department at Rice University.
Book Synopsis The Numerical Solution of Certain Partial Differential Equations and Related Eigenvalue Problem for Convex Regions by : Neal Owen Reinders
Download or read book The Numerical Solution of Certain Partial Differential Equations and Related Eigenvalue Problem for Convex Regions written by Neal Owen Reinders and published by . This book was released on 1959 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homotopy Continuation Method for Nonlinear Equations by : Mahmoud Mohseni Moghadam
Download or read book Homotopy Continuation Method for Nonlinear Equations written by Mahmoud Mohseni Moghadam and published by . This book was released on 1984 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:
