Some Approximate Methods for the Solution of Differential Equations
Author : Ernest Allan Miller
Publisher :
Page : 36 pages
File Size : 44,78 MB
Release : 1899
Category :
ISBN :
Approximate Methods of Solution of Differential Equations
Author : Instytut matematyky (Akademii︠a︡ nauk Ukraïnsʹkoï RSR)
Publisher :
Page : 236 pages
File Size : 38,62 MB
Release : 1967
Category : Differential equations
ISBN :
Book Description
Approximate Analytical Methods for Solving Ordinary Differential Equations
Author : T.S.L Radhika
Publisher : CRC Press
Page : 200 pages
File Size : 35,70 MB
Release : 2014-11-21
Category : Mathematics
ISBN : 1466588160
Book Description
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
Approximate Methods for Solution of Differential and Integral Equations
Author : Solomon Grigorʹevich Mikhlin
Publisher :
Page : 328 pages
File Size : 38,60 MB
Release : 1967
Category : Mathematics
ISBN :
Book Description
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.
Numerical Solution Of Ordinary And Partial Differential Equations, The (3rd Edition)
Author : Granville Sewell
Publisher : World Scientific
Page : 346 pages
File Size : 45,92 MB
Release : 2014-12-16
Category : Mathematics
ISBN : 9814635111
Book Description
This book presents methods for the computational solution of differential equations, both ordinary and partial, time-dependent and steady-state. Finite difference methods are introduced and analyzed in the first four chapters, and finite element methods are studied in chapter five. A very general-purpose and widely-used finite element program, PDE2D, which implements many of the methods studied in the earlier chapters, is presented and documented in Appendix A.The book contains the relevant theory and error analysis for most of the methods studied, but also emphasizes the practical aspects involved in implementing the methods. Students using this book will actually see and write programs (FORTRAN or MATLAB) for solving ordinary and partial differential equations, using both finite differences and finite elements. In addition, they will be able to solve very difficult partial differential equations using the software PDE2D, presented in Appendix A. PDE2D solves very general steady-state, time-dependent and eigenvalue PDE systems, in 1D intervals, general 2D regions, and a wide range of simple 3D regions.The Windows version of PDE2D comes free with every purchase of this book. More information at www.pde2d.com/contact.
Analysis of Approximation Methods for Differential and Integral Equations
Author : Hans-Jürgen Reinhardt
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 26,71 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461210801
Book Description
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.
Nonlinear Ordinary Differential Equations
Author : Martin Hermann
Publisher : Springer
Page : 320 pages
File Size : 26,11 MB
Release : 2016-05-09
Category : Mathematics
ISBN : 813222812X
Book Description
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 ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.
Approximation Methods for Solutions of Differential and Integral Equations
Author : V. K. Dzyadyk
Publisher : Walter de Gruyter GmbH & Co KG
Page : 332 pages
File Size : 22,46 MB
Release : 2018-11-05
Category : Mathematics
ISBN : 3110944693
Book Description
No detailed description available for "Approximation Methods for Solutions of Differential and Integral Equations".
Approximate Methods of Solution of Differential Equations (collection of Articles).
Author : FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO.
Publisher :
Page : 212 pages
File Size : 12,14 MB
Release : 1967
Category :
ISBN :
Book Description
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.
The Method of Weighted Residuals and Variational Principles
Author : Bruce A. Finlayson
Publisher : SIAM
Page : 429 pages
File Size : 16,82 MB
Release : 2013-12-30
Category : Mathematics
ISBN : 1611973236
Book Description
This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.
