Numerical Solutions of Boundary Value Problems with Finite Difference Method

This 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.

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.