Numerical Solutions Using the Taylor Series Method: Initial and Boundary Value Problems (Synthesis Lectures on Mathematics & Statistics) - Hardcover

Chowdhury, Sujaul; Moktadir, Md. Golam

Hardcover

ISBN 10: 3032269911 ISBN 13: 9783032269911

Publisher: Springer, 2026

Synopsis

This book discusses the Taylor Series Method for numerical solution of initial and boundary value problems.  A number of differential equations related to problems in physics have been solved numerically, including radioactive decay; simple harmonic motion; damped harmonic motion; driven damped harmonic motion; motion of oscillators in phase space, cyclotron motion; and differential equations for Hyperbolic functions.  In addition, several Hermite polynomials have been reproduced by numerically solving two-point boundary value problems.  Regarding oscillatory motion, the authors present both velocity and displacement of the oscillating particle as functions of time.  For cyclotron motion, the authors simulate trajectory of electrons in magnetic field in real space.  Also, Hermite polynomials H3, H4 and H5 are reproduced by numerically solving two-point boundary value problems.

About this title

About the Author

Sujaul Chowdhury, Ph.D., is a Professor in Department of Physics at Shahjalal University of Science and Technology. He received his B.Sc. and M.Sc. in Physics from Shahjalal University of Science and Technology, before earning his Ph.D. at The University of Glasgow in 2001. After completing his Ph.D., Dr. Chowdhury was a Humboldt Research Fellow for one year at The Max Planck Institute, Stuttgart. He is the author of many books, including six others with Springer: Monte Carlo Methods: A Hands-On Computational Introduction Utilizing Excel; Monte Carlo Methods Utilizing Mathematica®: Applications in Inverse Transform and Acceptance-Rejection Sampling; Numerical Exploration of Fourier Transform and Fourier Series: The Power Spectrum of Driven Damped Oscillators; Newtonian Mechanics; Numerical Exploration of Isolated GaAs-AlGaAs Quantum Well; and Introduction to Electronics. His research interests include nanoelectronics, magnetotransport in semiconductor nanostructures, and nanostructure physics.

Md. Golam Moktadir was a M.S. student in the Department of Physics at Shahjalal University of Science and Technology.

From the Back Cover

This book discusses the Taylor Series Method for numerical solution of initial and boundary value problems. A number of differential equations related to problems in physics have been solved numerically, including radioactive decay; simple harmonic motion; damped harmonic motion; driven damped harmonic motion; motion of oscillators in phase space, cyclotron motion; and differential equations for Hyperbolic functions. In addition, several Hermite polynomials have been reproduced by numerically solving two-point boundary value problems.  Regarding oscillatory motion, the authors present both velocity and displacement of the oscillating particle as functions of time. For cyclotron motion, the authors simulate trajectory of electrons in magnetic field in real space. Also, Hermite polynomials H3, H4 and H5 are reproduced by numerically solving two-point boundary value problems.

In addition, this book:

• Utilizes Mathematica® throughout to perform symbolic computation
• Demonstrates that large increments of the independent variable can be used to obtain agreement with analytic solutions
• Presents solutions of boundary value problems using the shooting method

Edition details

• Publisher: Springer
• Publication date: 2026
• Language: English
• ISBN 10: 3032269911
• ISBN 13: 9783032269911
• Binding: Hardcover
• Number of pages: 119