A Method Of Lines In The Numerical Solution Of Schr Dinger Equation
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A Method Of Lines In The Numerical Solution Of Schr Dinger Equation
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Author : Lawal Sa'adu
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012
A Method Of Lines In The Numerical Solution Of Schr Dinger Equation written by Lawal Sa'adu and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Differential equations, Partial categories.
The Method of Lines (MOL) has been one of the simplest but effective technique for solving partial differential equations (PDEs) in which all but one dimension is discretized. This work describes numerical solution of 1-dimensional Schrodinger equation using the method of lines approach (MOL) where spatial dimensions were discretized using some finite difference approximation leaving the time dimension to be the only independent variable in the resulting system of initial value problems. The effect of changing the discretization size on the accuracy of the solution procedure versus changing the step size in the integration of the resulting differential equation was also studied with the incorporation of Simpson's rule function in MATLAB.
Adaptive Method Of Lines
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Author : A. Vande Wouwer
language : en
Publisher: CRC Press
Release Date : 2001-04-18
Adaptive Method Of Lines written by A. Vande Wouwer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-18 with Mathematics categories.
The general Method of Lines (MOL) procedure provides a flexible format for the solution of all the major classes of partial differential equations (PDEs) and is particularly well suited to evolutionary, nonlinear wave PDEs. Despite its utility, however, there are relatively few texts that explore it at a more advanced level and reflect the method's
Numerical Methods For Initial Value Problems In Physics
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Author : Francisco S. Guzmán
language : en
Publisher: Springer Nature
Release Date : 2023-08-23
Numerical Methods For Initial Value Problems In Physics written by Francisco S. Guzmán and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-23 with Science categories.
This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs). Beginning with IVPs involving Ordinary Differential Equations (ODEs) and progressing to problems with Partial Differential Equations (PDEs) in 1+1 and 3+1 dimensions, it provides readers with a clear and systematic progression from simple to complex concepts. The numerical methods selected in this textbook can solve a considerable variety of problems and the applications presented cover a wide range of topics, including population dynamics, chaos, celestial mechanics, geophysics, astrophysics, and more. Each chapter contains a variety of solved problems and exercises, with code included. These examples are designed to motivate and inspire readers to delve deeper into the state-of-the-art problems in their own fields. The code is written in Fortran 90, in a library-free style, making them easy to program and efficient to run. The appendix also includes the same code in C++, making the book accessible to a variety of programming backgrounds. At the end of each chapter, there are brief descriptions of how the methods could be improved, along with one or two projects that can be developed with the methods and codes described. These projects are highly engaging, from synchronization of chaos and message encryption to gravitational waves emitted by a binary system and non-linear absorption of a scalar field. With its clear explanations, hands-on approach, and practical examples, this textbook is an essential resource for advanced undergraduate and graduate students who want to the learn how to use numerical methods to tackle challenging problems.
Information Computing And Applications
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Author : Chunfeng Liu
language : en
Publisher: Springer
Release Date : 2011-12-18
Information Computing And Applications written by Chunfeng Liu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-18 with Computers categories.
The two-volume set, CCIS 243 and CCIS 244, constitutes the refereed proceedings of the Second International Conference on Information Computing and Applications, ICICA 2010, held in Qinhuangdao, China, in October 2011. The 191 papers presented in both volumes were carefully reviewed and selected from numerous submissions. They are organized in topical sections on computational statistics, social networking and computing, evolutionary computing and applications, information education and application, internet and web computing, scientific and engineering computing, system simulation computing, bio-inspired and DNA computing, internet and Web computing, multimedia networking and computing, parallel and distributed computing.
Mathematical Methods For Geophysics And Space Physics
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Author : William I. Newman
language : en
Publisher: Princeton University Press
Release Date : 2016-05-03
Mathematical Methods For Geophysics And Space Physics written by William I. Newman and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-03 with Science categories.
Graduate students in the natural sciences—including not only geophysics and space physics but also atmospheric and planetary physics, ocean sciences, and astronomy—need a broad-based mathematical toolbox to facilitate their research. In addition, they need to survey a wider array of mathematical methods that, while outside their particular areas of expertise, are important in related ones. While it is unrealistic to expect them to develop an encyclopedic knowledge of all the methods that are out there, they need to know how and where to obtain reliable and effective insights into these broader areas. Here at last is a graduate textbook that provides these students with the mathematical skills they need to succeed in today's highly interdisciplinary research environment. This authoritative and accessible book covers everything from the elements of vector and tensor analysis to ordinary differential equations, special functions, and chaos and fractals. Other topics include integral transforms, complex analysis, and inverse theory; partial differential equations of mathematical geophysics; probability, statistics, and computational methods; and much more. Proven in the classroom, Mathematical Methods for Geophysics and Space Physics features numerous exercises throughout as well as suggestions for further reading. Provides an authoritative and accessible introduction to the subject Covers vector and tensor analysis, ordinary differential equations, integrals and approximations, Fourier transforms, diffusion and dispersion, sound waves and perturbation theory, randomness in data, and a host of other topics Features numerous exercises throughout Ideal for students and researchers alike An online illustration package is available to professors
Information Computing And Applications
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Author : Yuhang Yang
language : en
Publisher: Springer
Release Date : 2013-12-20
Information Computing And Applications written by Yuhang Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Computers categories.
This two-volume set of CCIS 391 and CCIS 392 constitutes the refereed proceedings of the Fourth International Conference on Information Computing and Applications, ICICA 2013, held in Singapore, in August 2013. The 126 revised full papers presented in both volumes were carefully reviewed and selected from 665 submissions. The papers are organized in topical sections on Internet computing and applications; engineering management and applications; intelligent computing and applications; control engineering and applications; cloud and evolutionary computing; knowledge management and applications; computational statistics and applications.
Frontiers And Prospects Of Contemporary Applied Mathematics
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Author : Pingwen Zhang
language : en
Publisher: World Scientific
Release Date : 2006-04-17
Frontiers And Prospects Of Contemporary Applied Mathematics written by Pingwen Zhang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-17 with Mathematics categories.
This collection of articles covers the hottest topics in contemporary applied mathematics. Multiscale modeling, material computing, symplectic methods, parallel computing, mathematical biology, applied differential equations and engineering computing problems are all included. The book contains the latest results of many leading scientists and provides a window on new trends in research in the field.
Artificial Boundary Method
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Author : Houde Han
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-13
Artificial Boundary Method written by Houde Han and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-13 with Mathematics categories.
"Artificial Boundary Method" systematically introduces the artificial boundary method for the numerical solutions of partial differential equations in unbounded domains. Detailed discussions treat different types of problems, including Laplace, Helmholtz, heat, Schrödinger, and Navier and Stokes equations. Both numerical methods and error analysis are discussed. The book is intended for researchers working in the fields of computational mathematics and mechanical engineering. Prof. Houde Han works at Tsinghua University, China; Prof. Xiaonan Wu works at Hong Kong Baptist University, China.
The Mathematica Guidebook For Numerics
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Author : Michael Trott
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-27
The Mathematica Guidebook For Numerics written by Michael Trott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-27 with Computers categories.
Provides the reader with working knowledge of Mathematica and key aspects of Mathematica's numerical capabilities needed to deal with virtually any "real life" problem Clear organization, complete topic coverage, and an accessible writing style for both novices and experts Website for book with additional materials: http://www.MathematicaGuideBooks.org Accompanying DVD containing all materials as an electronic book with complete, executable Mathematica 5.1 compatible code and programs, rendered color graphics, and animations
Computational Mathematics In Engineering And Applied Science
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Author : W.E. Schiesser
language : en
Publisher: CRC Press
Release Date : 2014-07-22
Computational Mathematics In Engineering And Applied Science written by W.E. Schiesser and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Mathematics categories.
Computational Mathematics in Engineering and Applied Science provides numerical algorithms and associated software for solving a spectrum of problems in ordinary differential equations (ODEs), differential algebraic equations (DAEs), and partial differential equations (PDEs) that occur in science and engineering. It presents detailed examples, each