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Friday, July 31, 2020 | History

3 edition of Non-linear equations. found in the catalog.

Non-linear equations.

Open University. Numerical Computation Course Team.

Non-linear equations.

by Open University. Numerical Computation Course Team.

  • 3 Want to read
  • 23 Currently reading

Published by Open University Press in Milton Keynes .
Written in English


Edition Notes

SeriesMathematics, a third level course, Numerical Computation; unit 2, M351; unit 2
ID Numbers
Open LibraryOL21643331M

D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, An Introduction to Dynamical Systems (4th Edition, Oxford University Press, ) I am sure you can learn a lot even on your. "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.

  Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in , due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications. Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods.

used textbook “Elementary differential equations and boundary value problems” by Boyce & DiPrima (John Wiley & Sons, Inc., Seventh Edition, c ). Many of the examples presented in these notes may be found in this book. The material of Chapter 7 is adapted from the textbook “Nonlinear dynamics and chaos” by Steven. The problem of solving non-linear equations arises frequently and naturally from the study of a wide range of practical problems. The problem may involve one or a system of non-linear equations in many variables. In this chapter, general methods of solving non-linear equations are presented, together with specific methods for polynomial equations.


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Non-linear equations by Open University. Numerical Computation Course Team. Download PDF EPUB FB2

Non-linear elliptic partial differential equations are an important tool in the study of Riemannian metrics in differential geometry, in particular for problems concerning the conformal change of metrics in Riemannian by: Non-linear Equations, Quantum Groups and Duality Non-linear equations.

book A primer on the Yang-Baxter equation Buy used On clicking this link, a new layer will be open $ On clicking this link, a new layer will be open Buy new On clicking this link, a new layer will be open $ On clicking this link, a new layer. Non-linear ordinary differential equations are stiff and can be solved numerically, but numerical solutions do not provide physical parametric insight.

Consequently, it is often necessary to find a closed analytical by: This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and Non-linear equations.

book equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations Cited by: Non-Linear Differential Equations covers the general theorems, principles, solutions, and applications of non-linear differential equations.

This book is divided into nine chapters. The first chapters contain detailed analysis of the phase portrait of two-dimensional autonomous systems. The first chapter gives a taste of some of the solution techniques of some ODE's, and the rest is working on those techniques. The entire book is devoted to a motivating writing style in the sense that you are introduced to a concept or an idea in a very general sense, you get some background, a little history, Cited by: This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations.

Parts of this book are based upon work supported bythe National Science Foundation and the Air Force Office of Scientific Research over several years, most recently under National Science Foundation Grant Nos.

DMSandDMS Anyopinions,findings,andconclusionsor recommendationsexpressedinthismaterialarethoseoftheauthoranddonotFile Size: KB. The subject of Differential Equations is a well established part of mathe-matics and its systematic development goes back to the early days of the de-velopment of Calculus.

Many recent advances in mathematics, paralleled by a renewed and flourishing interaction between. As nonlinear dynamical equations are difficult to solve, nonlinear systems are commonly approximated by linear equations (linearization).

This works well up to some accuracy and some range for the input values, but some interesting phenomena such as solitons, chaos, and singularities are hidden by linearization. It follows that some aspects of the dynamic behavior of a nonlinear system. 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.

1 Introduction. Formulation of the problem. Linear algebra [1] is one of the foundations of modern natural science: whereverwe are interested in calculations, from.

engineering to string theory, we use linear equations, quadratic forms, matrices, linear maps and their by: Non-linear rst order ODE Non-linear equations are signi cantly more di cult.

We will study rst order ODE’s of the form y0= f(x;y). An existence and uniqueness theorem covering most examples is the following. Let Iand Jbe open intervals in R with values x 0 2Iand y 0 2J.

Let RˆR2 be the rectangle of all points (x;y) with x2Iand y2J. First note that, unlike systems of linear equations, it is possible for a system of non-linear equations to have more than one solution without having infinitely many solutions.

In fact, while we characterize systems of nonlinear equations as being `consistent' or `inconsistent,' we generally don't use the labels `dependent' or `independent'. On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature.

The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets andBrand: Springer-Verlag Berlin Heidelberg. This book discusses as well nonlinear hyperbolic equations in further contributions, featuring stability properties of periodic and almost periodic solutions.

The reader is also introduced to the stability problem of the equilibrium of a chemical network. The final chapter deals with suitable spaces for studying functional equations. This book covers the following topics: Geometry and a Linear Function, Fredholm Alternative Theorems, Separable Kernels, The Kernel is Small, Ordinary Differential Equations, Differential Operators and Their Adjoints, G(x,t) in the First and Second Alternative and Partial Differential Equations.

Linear or Non-linear Systems (Linearity Property): A linear system is a system which follows the superposition principle. Let us consider a system having its response as ‘T’, input as x(n) and it produces output y(n). This is shown in figure below: Let us consider two inputs.

Input x1(n) produces output y1(n) and input x2(n) produces. Concise introduction to a relatively new subject of non-linear algebra: literal extension of text-book linear algebra to the case of non-linear equations and maps.

This powerful science is based on the notions of discriminant (hyperdeterminant) and resultant, which today can be effectively studied both analytically and by modern computer facilities.

The paper is mostly focused on resultants of Cited by: BACKGROUND. Equations need to be solved in all areas of science and engineering.

An equation of one variable can be written in the form: A solution to the equation (also called a root of the equation) is a numerical value of x that satisfies the equation.

Graphically, as shown in Fig.the solution is the point where the function f(x) crosses or touches the x-axis. Non-Linear Equations The aim of this chapter is to discuss the most useful methods for finding the roots of any equation having numerical coefficients.

Polynomial equations of degree ≤ 4 can be solved by standard algebraic methods.This second edition provides much-needed updates to the original volume.

Like the first edition, it emphasizes the ideas behind the algorithms as well as their theoretical foundations and properties, rather than focusing strictly on computational details; at the same time, this new version is now largely self-contained and includes essential proofs.

Non-Linear Differential Equations and Dynamical Systems is the second book within Ordinary Differential Equations with Applications to Trajectories and Vibrations, Six-volume a set, they are the fourth volume in the series Mathematics and Physics Applied to Science and second book consists of two chapters (chapters 3 and 4 of the set).Price: $