1 edition of Approximate methods for functional differential equations found in the catalog.
Approximate methods for functional differential equations
|Series||Monografie / Politechnika Gdańska -- 92|
|LC Classifications||QA297.5 .B37 2009|
|The Physical Object|
|Pagination||171 p. :|
|Number of Pages||171|
|LC Control Number||2012381016|
This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman () Functional Data central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led. The subject is interesting on its own, but aside from the abstract interest, it's ultimately because we want to use those methods to understand power series solutions of differential equations. The Simmons book is clearly written, and it not only makes the subject interesting but deeply fascinating.
In scientific computation and simulation, the method of fundamental solutions (MFS) is a technique for solving partial differential equations based on using the fundamental solution as a basis function. A modification of the collocation method Is proposed for use In the approximate solution of the Cauchy problem for a system of ordinary differential equations, the Goursat problem for systems of hyperbolic equations and the first ^ boundary-value problem for a non-stationary system of Navler- Stokes equations.
Book Description. Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. The differential equations we consider in most of the book are of the form Y′(t) = f(t,Y(t)), where Y(t) is an unknown function that is being sought. The given function f(t,y) of two variables deﬁnes the differential equation, and exam ples are given in Chapter 1. This equation is called a ﬁrst-order differential equation because it File Size: 1MB.
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Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles.
It covers both well-established techniques and recently developed procedures, including the classical series solutCited by: 6. Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles.
It covers both well-established techniques and recently developed procedures, including the classical series solution method, diverse perturbation methods, pioneering asymptotic methods, and the latest homotopy methods. This is the first comprehensive introduction to collocation methods for the numerical solution of initial-value problems for ordinary differential equations, Volterra integral and integro-differential equations, and various classes of more general functional : Hardcover.
The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations.
The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for. method on the high-order li near pantograph-type functional differential equations with mixed proportional and variable delays.
All the problems have been calculated by usingAuthor: Burcu Gürbüz. The numerical results show that the proposed method is of a high accuracy and is efficient for solving a wide class of functional-differential equations with proportional delays including equations of neutral type.
The method is applicable to both initial and boundary value problems. The Numerical Approximation of Functional Differential Equations by Daniele Venturi. Publisher: arXiv Number of pages: Description: The purpose of this manuscript is to provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations.
From Tables 1–3, we can see that the precision is improved greatly compared with Runge–Kutta method and variational iteration numerical results also show that the present method yields a very effective and convenient approach to the approximate solution of neutral functional–differential equations with proportional by: 3.
The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7, ordinary.
Value Problems” and “Functional Diﬀerential Equations” issued in – by the Perm Polytechnic Institute. In the book, only the works closely related to the questions under considera-tion are cited.
It is assumed that the reader is acquainted with the foundations of functional analysis. Let us give some remarks on the by: This book explains the following topics: First Order Equations, Numerical Methods, Applications of First Order Equations1em, Linear Second Order Equations, Applcations of Linear Second Order Equations, Series Solutions of Linear Second Order Equations, Laplace Transforms, Linear Higher Order Equations, Linear Systems of Differential Equations, Boundary Value Problems and Fourier.
The paper presents a new numerical method for solving functional differential equations with proportional delays of the first and higher orders. The method consists of replacing the initial equation by an approximate equation which has an exact analytic solution with a set of free by: 8.
Set-valued and fuzzy stochastic differential equations in M-type 2 Banach spaces Malinowski, Marek T., Tohoku Mathematical Journal, ; Monotone-Iterative Method for the Initial Value Problem with Initial Time Difference for Differential Equations with “Maxima” Hristova, S.
and Golev, A., Abstract and Applied Analysis, Cited by: The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods.
That is, a functional differential equation is an equation that contains some function and some of its derivatives to different argument values.  Functional differential equations find use in mathematical models that assume a specified behavior or phenomenon depends on the present as well as the past state of a system.
. The chapters on the functional linear model and modeling of the dynamics of systems through the use of differential equations and principal differential analysis have been completely rewritten and extended to include new developments.
Other chapters have been revised substantially, often to give more weight to examples and practical considerations. Turo discussed the Carathéodory approximate solution of stochastic functional differential equations (SFDEs) and established the existence theorem for SFDEs.
Liu [ 18 ] investigated a class of semilinear stochastic evolution equations with time delays and proved that the Carathéodory approximate solution converges to the solution of stochastic delay evolution by: 3.
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear by: 7.
Definitely the best intro book on ODEs that I've read is Ordinary Differential Equations by Tenebaum and Pollard. Dover books has a reprint of the book for maybe dollars on Amazon, and considering it has answers to most of the problems found.
Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations.
Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in. In this paper, a collocation method using sinc functions and Chebyshev wavelet method is implemented to solve linear systems of Volterra integro-differential equations.
To test the validity of these methods, two numerical examples with known exact solution are presented. Numerical results indicate that the convergence and accuracy of these methods are in good a agreement with the analytical Author: Ahmad Issa, Naji Qatanani, Adnan Daraghmeh.The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology.
This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential : G. Gripenberg, S.
O. Londen, O. Staffans. Collocation based on piecewise polynomial approximation represents a powerful class of methods for the numerical solution of initial-value problems for functional differential and integral equations arising in a wide spectrum of applications, including biological and physical phenomena.
The present book introduces the reader to the general principles underlying these methods and then .