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Tuesday, July 28, 2020 | History

5 edition of The numerical treatment of a single nonlinear equation found in the catalog.

The numerical treatment of a single nonlinear equation

by Alston Scott Householder

  • 251 Want to read
  • 0 Currently reading

Published by McGraw-Hill in New York .
Written in English

    Subjects:
  • Equations -- Numerical solutions.,
  • Nonlinear theories.

  • Edition Notes

    Bibliography: p. 193-214.

    Statement[by] A. S. Householder.
    SeriesInternational series in pure and applied mathematics
    Classifications
    LC ClassificationsQA218 .H68
    The Physical Object
    Paginationviii, 216 p.
    Number of Pages216
    ID Numbers
    Open LibraryOL4442354M
    LC Control Number79103908

    Ordinary differential equations are a happy family; perhaps they do not resemble each other but, at the very least, we can write them in a single overarching form y ′ = f (t, y) and treat them by a relatively small compendium of computational techniques. (True, upon closer examination, even ODEs are not all the same: their classification into. I have been reading the Strogatz book on Nonlinear Ordinary Differential equations and I understand the graphical/qualitative method to solving these types of equations. However, Strogatz did not seem to address the role of numerical methods in solving nonlinear ODEs or systems of ODEs.

    Introduction to Differential Equation Solving with DSolve The Mathematica function DSolve finds symbolic solutions to differential equations. (The Mathe- matica function NDSolve, on the other hand, is a general numerical differential equation solver.) DSolve can handle the following types of equations: † Ordinary Differential Equations (ODEs), in which there is a single independent variable. The need to predict, understand, and optimize complex physical and c- mical processes occurring in and around the earth, such as groundwater c- tamination, oil reservoir production, discovering new oil reserves, and ocean hydrodynamics, has been increasingly recognized. Despite their seemingly disparate natures, these geoscience problems have many common mathe- tical and computational.

    Single Nonlinear Algebraic Equations and Systems of Nonlinear Algebraic Equations David Keffer Department of Chemical Engineering University of Tennessee, Knoxville June Table of Contents Introduction 1 I. Single Non-linear Algebraic Equation, Advanced Numerical Techniques 2 A. Newton Raphson Method with Numerical Derivatives 2 Example. conditions of solution existence of the linear VIE with jump discontinuity on the single curve were derived by Denisov and Lorenzi [5]. The papers [6–8] are devoted to a numerical treatment of integral dynamical systems described, using the nonlinear Volterra integral equations with unknown functions.


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The numerical treatment of a single nonlinear equation by Alston Scott Householder Download PDF EPUB FB2

Numerical Treatment of a Single Nonlinear Equation (Pure & Applied Mathematics) Hardcover – June 1, by Householder, (Author) out of 5 stars 1 rating4/5(1). The Numerical Treatment of a Single Nonlinear Equation [Alston S. Householder] on *FREE* shipping on qualifying offers.

The Numerical Treatment of a Single Nonlinear Equation4/5(1). The numerical treatment of a single nonlinear equation by Householder, Alston Scott, Pages: Book Title The numerical treatment of a single nonlinear equation: Author(s) Householder, Alston S: Publication New York, NY: McGraw-Hill, - p.

Series (International series in pure and applied mathematics) Subject code ; Subject category Mathematical Physics and Mathematics.

Corpus ID: The numerical treatment of a single nonlinear equation @inproceedings{HouseholderTheNT, title={The numerical treatment of a single nonlinear equation}, author={Alston S. Householder}, year={} }.The numerical treatment of a single nonlinear equation [by] A.

Householder McGraw-Hill New York Wikipedia Citation Please see Wikipedia's template documentation for. This book is composed of 10 chapters and begins with the concepts of nonlinear algebraic equations in continuum mechanics.

The succeeding chapters deal with the numerical solution of quasilinear elliptic equations, the nonlinear systems in semi-infinite programming, and the solution of large systems of linear algebraic equations. Lecture Notes on Numerical Analysis of Nonlinear Equations.

This book covers the following topics: The Implicit Function Theorem, A Predator-Prey Model, The Gelfand-Bratu Problem, Numerical Continuation, Following Folds, Numerical Treatment of Bifurcations, Examples of Bifurcations, Boundary Value Problems, Orthogonal Collocation, Hopf Bifurcation and Periodic Solutions, Computing Periodic Solutions, Periodic Orbit Folds, Stable and Unstable Manifolds.

Numerical methods are used to approximate solutions of equations when exact In Mathwe focused on solving nonlinear equations involving only a single vari-able.

We used methods such as Newton’s method, the Secant method, and the Bisection method. We also examined numerical methods such as the Runge-Kutta methods, that. Numerical Methods I Solving Nonlinear Equations Aleksandar Donev Courant Institute, NYU1 [email protected] 1Course G / G, Fall October 14th, A.

Donev (Courant Institute) Lecture VI 10/14/ 1 / It might be thought that this is a remarkable result, that the Euler equations, the set of three nonlinear dynamic equations of fluid dynamics can be reduced to a single partial differential equation, linear in the dependent variable φ.

The boundary conditions of the flow problem must be introduced so. Search within book. Front Matter. Pages II-XV. PDF. As yet, the numerical treatment of differential equations has been investigated far too little, bothin both in theoretical theoretical and and practical practical respects, respects, and and approximate approximate methods methods need need to to be be tried tried out out to to a a far far.

Numerical treatment of a single nonlinear equation. New York, McGraw-Hill [] (OCoLC) Material Type: Internet resource: Document Type: Book, Internet Resource: All Authors / Contributors: Alston Scott Householder.

ordinary differential equations for upper-division undergraduate students and begin-ning graduate students in mathematics, engineering, and sciences.

The book intro-duces the numerical analysis of differential equations, describing the mathematical background for understanding numerical methods and giving information on what to expect when.

Get this from a library. The numerical treatment of a single nonlinear equation. [Alston S Householder]. A treatment of nonhomogeneous systems follows, extending the methods introduced in Chapter 4 for single nonhomogeneous equations.

Spring-mass problems are analyzed from a qualitative point of view. Finally, ideas previously developed are extended to nth-order equations and their equivalent systems. engineering, medicine and business. A new iterative method for nding the approximate solutions of the nonlinear equation (x) = 0.

This numerical method has been constructed using di erent techniques such as Taylor series, homotopy, quadrature The Numerical Treatment of a single Nonlinear Equation, McGraw-Hill, New York, ().

This paper concerns through the numerical treatment of Fisher's reaction-diffusion equation by using a hybrid numerical method. than nonlinear equations encountered in science and.

Numerical tests shows that the new method is comparable with the well-known existing single step iterative methods and provides better results. Keywords: Nonlinear equations, iterative methods, Simpson method, Newton’s method, convergence.

c JS Publication. The numerical treatment of the NLS equations 71 Table 1 4 0 11 u"11 N lul= VZ+Wz R Fig. 1 It is shown that from Table 1, the method is exactly conservative.

Householder: The Numerical Treatment of a Single Nonlinear Equation Kalman, Falb, and Arbib: Topics in Mathematical Systems Theory McCarty: Topology: An Introduction with Applications to Topological Groups Moore: Elements of Linear Algebra and Matrix Theory Moursund and Duris: Elementary Theory and Application of Numerical Analysis.systems of nonlinear algebraic equations represent just a few of the applications of numerical linear algebra.

Because of this prevalence of numerical linear algebra, we begin our treatment of basic numerical methods with this topic, and note that this is somewhat nonstandard.Nonlinear elliptic problems play an increasingly important role in mathematics, science and engineering, and create an exciting interplay.

Other books discuss nonlinearity by a very few important examples. This is the first and only book, proving in a systematic and unifying way, stability and convergence results and methods for solving nonlinear discrete equations via discrete Newton methods.