Approximate Analytical Methods for Solving Ordinary Differential Equations

Approximate Analytical Methods for Solving Ordinary Differential Equations PDF

Author: T.S.L Radhika

Publisher: CRC Press

Published: 2014-11-21

Total Pages: 200

ISBN-13: 1466588160

DOWNLOAD EBOOK →

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 solut

Analysis of Approximation Methods for Differential and Integral Equations

Analysis of Approximation Methods for Differential and Integral Equations PDF

Author: Hans-Jürgen Reinhardt

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 412

ISBN-13: 1461210801

DOWNLOAD EBOOK →

This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.

Approximate Methods for Solution of Differential and Integral Equations

Approximate Methods for Solution of Differential and Integral Equations PDF

Author: Solomon Grigorʹevich Mikhlin

Publisher:

Published: 1967

Total Pages: 328

ISBN-13:

DOWNLOAD EBOOK →

The aim of this book is to acquaint the reader with the most important and powerful methods of approximate solution of boundary-value problems (including the Cauchy problem) for differential equations, both ordinary and partial, as well as approximate methods for solution of the most frequently encountered types of integral equations: Fredholm, Volterra and singular one-dimensional. This covers the entire domain of classical applications of mathematical analysis to mechanics, engineering, and mathematical physics.

Approximate Methods of Solution of Differential Equations (collection of Articles).

Approximate Methods of Solution of Differential Equations (collection of Articles). PDF

Author: FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO.

Publisher:

Published: 1967

Total Pages: 212

ISBN-13:

DOWNLOAD EBOOK →

Contents: Application of method of small parameter to analysis of hypersonic flow of gas around flat bodies; Influence of hysteresis motor on stability of motion of gyroscope in cardan joint suspension; On numerical solution of three-dimensional boundary value problems of theory of potential by method of sum representations; Concerning the question of stability of motion in one case of the three bodies; Certain questions of asymptotic solution of one operator differential equation; On the influence of random forces on nonlinear oscillatory systems; Sufficient conditions of convergence of method of Yu. D. Sokolov during approximate solution of nonlinear integral equations of type of Hammerstein; On the cauchy problem for equations of higher order with multiple characteristics; On random processes in simple linear delay systems; Random shocks in linear dynamic systems; On adherence of solutions of a linear uniform second order delay differential equation; Substantiation of principle of averaging for differential equations with discontinuous right side; Asymptotic behavior of negative part of spectrum of one-dimensional differential operators; Appearance of theory of potential of double layer and its first applications to solution of certain boundary value problems; On the solution of a type of nonlinear differential equation; On the existence and properties of integral manifold for system of nonlinear delay differential equations with variable coefficients; On nonlinear oscillations of a plate.

Numerical Approximation of Partial Differential Equations

Numerical Approximation of Partial Differential Equations PDF

Author: Alfio Quarteroni

Publisher: Springer Science & Business Media

Published: 2009-02-11

Total Pages: 551

ISBN-13: 3540852689

DOWNLOAD EBOOK →

Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Lanterna Rally - Theme by Grace Themes