Numerical solutions of boundary value problems with finite difference method /

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"Version: 20180901"--Title page verso."A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.Includes bibliographical references.1. A numerical solution of boundary value problem using the finite difference method -- 1.1. Statement of the problem -- 1.2. Approximation to derivatives -- 1.3. The finite difference method2. Differential equations of some elementary functions : boundary value problems numerically solved using finite difference method -- 2.1. The differential equation for hyperbolic function -- 2.2. The differential equation for Cosine function -- 2.3. The differential equation for Sine function3. Differential equations of special functions : boundary value problems numerically solved using finite difference method -- 3.1. The Hermite differential equation -- 3.2. The Laguerre differential equation -- 3.3. The Legendre differential equation4. Differential equation of Airy function : boundary value problem numerically solved using finite difference method -- 4.1. The differential equation for Airy function5. Differential equation of stationary localised wavepacket : boundary value problem numerically solved using finite difference method -- 5.1. Differential equation for stationary localised wavepacket6. Particle in a box : boundary value problem numerically solved using finite difference method -- 6.1. The quantum mechanical problem of a particle in a one-dimensional box7. Motion under gravitational interaction : boundary value problem numerically solved using finite difference method -- 7.1. Motion under gravitational interaction -- 8. Concluding remarks.The book contains an extensive illustration of use of finite difference method in solving the boundary value problem numerically. A wide class of differential equations has been numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, we have solved those of special functions like Hermite, Laguerre and Legendre. Those of Airy function, of stationary localised wavepacket, of the quantum mechanical problem of a particle in a 1D box, and the polar equation of motion under gravitational interaction have also been solved. Mathematica 6.0 has been used to solve the system of linear equations that we encountered and to plot the numerical data. Comparison with known analytic solutions showed nearly perfect agreement in every case. On reading this book, readers will become adept in using the method.Undergraduate students of mathematics, physics and engineering wishing to get adept in numerical solutions of boundary value problems with finite difference method will be delighted to get this book or e-book.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Sujaul Chowdhury is a Professor in Department of Physics, Shahjalal University of Science and Technology (SUST), Bangladesh. He obtained a BSc (Honours) in physics in 1994 and MSc in physics in 1996 from SUST. He obtained a PhD in physics from The University of Glasgow, UK in 2001. He was a Humboldt Research Fellow for one year at The Max Planck Institute, Stuttgart, Germany. He is the author of the book Numerical Solutions of Initial Value Problems Using Mathematica. Ponkog Kumar Das is an Assistant Professor in Department of Physics, SUST. He obtained a BSc (Honours) and MSc in physics from SUST. He is a co-author of the book Numerical Solutions of Initial Value Problems Using Mathematica. Syed Badiuzzaman Faruque is a Professor in Department of Physics, SUST. He is a researcher with interest in quantum theory, gravitational physics, material science etc. He has been teaching physics at university level for about 26 years. He studied physics at The University of Dhaka, Bangladesh and The University of Massachusetts Dartmouth, and did a PhD in SUST.Title from PDF title page (viewed on October 16, 2018).

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Publisher

: .,

Collation

1 online resource (various pagings) :illustrations.

Language

English

ISBN/ISSN

9781643272801

Classification

515/.35

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Subject(s)

SCIENCE / Applied Sciences.
Applied physics.
Finite differences.
Boundary value problems

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Statement of Responsibility

Sujaul Chowdhury, Ponkog Kumar Das and Syed Badiuzzaman Faruque.

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