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An Operational Unification Of Finite Difference Methods For The Numerical Integration Of Ordinary Differential Equations
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Book Synopsis An Operational Unification of Finite Difference Methods for the Numerical Integration of Ordinary Differential Equations by : Harvard Lomax
Download or read book An Operational Unification of Finite Difference Methods for the Numerical Integration of Ordinary Differential Equations written by Harvard Lomax and published by . This book was released on 1967 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: One purpose of this report is to present a mathematical procedure which can be used to study and compare various numerical methods for integrating ordinary differential equations. This procedure is relatively simple, mathematically rigorous, and of such a nature that matters of interest in digital computations, such as machine memory and running time, can be weighed against the accuracy and stability provided by the method under consideration. Briefly, the procedure is as follows: (1) Find a single differential equation that is sufficiently representative (this is fully defined in the report) of an arbitrary number of nonhomogeneous, linear, ordinary differential equations with constant coefficients. (2) Solve this differential equation exactly. (3) Choose any given numerical method, use it -- in its entirety -- to reduce the differential equation to difference equations, and, by means of operational techniques, solve the latter exactly. (4) Study and compare the results of (2) and (3). Conceptually there is nothing new in this procedure, but the particular development presented in this report does not appear to have been carried out before. Another purpose is to use the procedure just described to analyze a variety of numerical methods, ranging from classical, predictor-corrector systems to Runge-Kutta techniques and including various combinations of the two.
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Book Synopsis An Operational Unification of Finite Difference Methods for the Numerical Integration of Ordinary Differential Equations by : Harvard Lomax
Download or read book An Operational Unification of Finite Difference Methods for the Numerical Integration of Ordinary Differential Equations written by Harvard Lomax and published by . This book was released on 1967 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonstandard Finite Difference Models of Differential Equations by : Ronald E. Mickens
Download or read book Nonstandard Finite Difference Models of Differential Equations written by Ronald E. Mickens and published by World Scientific. This book was released on 1994 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of ?exact? and ?best? finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation.
Book Synopsis Stable Implicit and Explicit Numerical Methods for Integrating Quasi-linear Differential Equations with Parasitic-stiff and Parasitic-saddle Eigenvalues by : Harvard Lomax
Download or read book Stable Implicit and Explicit Numerical Methods for Integrating Quasi-linear Differential Equations with Parasitic-stiff and Parasitic-saddle Eigenvalues written by Harvard Lomax and published by . This book was released on 1968 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Critical Analysis of Various Numerical Integration Methods for Computing the Flow of a Gas in Chemical Nonequilibrium by : Harvard Lomax
Download or read book A Critical Analysis of Various Numerical Integration Methods for Computing the Flow of a Gas in Chemical Nonequilibrium written by Harvard Lomax and published by . This book was released on 1967 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Construction of Highly Stable, Explicit, Numerical Methods for Integrating Coupled Ordinary Differential Equations with Parasitic Eigenvalues by : Harvard Lomax
Download or read book On the Construction of Highly Stable, Explicit, Numerical Methods for Integrating Coupled Ordinary Differential Equations with Parasitic Eigenvalues written by Harvard Lomax and published by . This book was released on 1968 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book NASA Technical Note written by and published by . This book was released on 1969 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1989 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book NASA Technical Report written by and published by . This book was released on 1969 with total page 1158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in the Applications of Nonstandard Finite Difference Schemes by : Ronald E Mickens
Download or read book Advances in the Applications of Nonstandard Finite Difference Schemes written by Ronald E Mickens and published by World Scientific. This book was released on 2005-10-25 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential equations occurring in the natural, biomedical, and engineering sciences. These methods had their genesis in the work of Mickens in the 1990's and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to advance the topic. Contents:Nonstandard Finite Difference Methods (R E Mickens)Application of Nonstandard Finite Difference Schemes to the Simulation Studies of Robotic Systems (R F Abo-Shanab et al.)Applications of Mickens Finite Differences to Several Related Boundary Value Problems (R Buckmire)High Accuracy Nonstandard Finite-Difference Time-Domain Algorithms for Computational Electromagnetics: Applications to Optics and Photonics (J B Cole)Nonstandard Finite Difference Schemes for Solving Nonlinear Micro Heat Transport Equations in Double-Layered Metal Thin Films Exposed to Ultrashort Pulsed Lasers (W Dai)Reliable Finite Difference Schemes with Applications in Mathematical Ecology (D T Dimitrov et al.)Applications of the Nonstandard Finite Difference Method in Non-Smooth Mechanics (Y Dumont)Finite Difference Schemes on Unbounded Domains (M Ehrhardt)Asymptotically Consistent Nonstandard Finite-Difference Methods for Solving Mathematical Models Arising in Population Biology (A B Gumel et al.)Nonstandard Finite Difference Methods and Biological Models (S R-J Jang)Robust Discretizations versus Increase of the Time Step for Chaotic Systems (C Letellier & E M A M Mendes)Contributions to the Theory of Nonstandard Finite-Difference Methods and Applications to Singular Perturbation Problems (J M-S Lubuma & K C Patidar)Frequency Accurate Finite Difference Methods (A L Perkins et al.)Nonstandard Discretization Methods on Lotka-Volterra Differential Equations (L-I W Roeger) Readership: Applied mathematicians, and researchers in numerical & computational mathematics and analysis & differential equations. Usable as a secondary text to a standard undergraduate or graduate course on numerical methods for differential equations. Keywords:Numerical Integration Methods;Finite Differences;Nonstandard Finite Difference Schemes;Differential Equations;Discrete Models;Numerical and Computational MathematicsKey Features:A collection of papers from renowned experts in their respective fieldsProvides the most recent work on the application of NSFD schemes and some of the mathematical analysis related to these schemes
Book Synopsis On Some Numerical Difficulties in Integrating the Equations for One-dimensional Nonequilibrium Nozzle Flow by : Harvard Lomax
Download or read book On Some Numerical Difficulties in Integrating the Equations for One-dimensional Nonequilibrium Nozzle Flow written by Harvard Lomax and published by . This book was released on 1969 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in the Applications of Nonstandard Finite Diffference Schemes by : Ronald E. Mickens
Download or read book Advances in the Applications of Nonstandard Finite Diffference Schemes written by Ronald E. Mickens and published by World Scientific. This book was released on 2005 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a concise introduction to the methodology of nonstandard finite difference (NSFD) schemes construction and shows how they can be applied to the numerical integration of differential equations occurring in the natural, biomedical, and engineering sciences. These methods had their genesis in the work of Mickens in the 1990's and are now beginning to be widely studied and applied by other researchers. The importance of the book derives from its clear and direct explanation of NSFD in the introductory chapter along with a broad discussion of the future directions needed to advance the topic.
Book Synopsis Fractional Differential Equations by : Zhi-Zhong Sun
Download or read book Fractional Differential Equations written by Zhi-Zhong Sun and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-24 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.
Download or read book ARS. written by and published by . This book was released on 1971 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Investigations on the Basic Theory of Static and Dynamic Pressure Phenomena in Grain Under Conditions of Storage by : Joel D. Isaacson
Download or read book Investigations on the Basic Theory of Static and Dynamic Pressure Phenomena in Grain Under Conditions of Storage written by Joel D. Isaacson and published by . This book was released on 1971 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Government-wide Index to Federal Research & Development Reports by :
Download or read book Government-wide Index to Federal Research & Development Reports written by and published by . This book was released on 1967-05 with total page 1472 pages. Available in PDF, EPUB and Kindle. Book excerpt:
