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Intended for graduate students in Mathematics and Physics, this book contains an extensive illustration of the use of finite-difference method in numerically solving boundary value problems with derivative boundary conditions. A wide class of differential equations have been numerically solved in this book. We start with differential equations of elementary functions such as Hyperbolic, Cosine and Sine, and solve those of special functions like Hermite, Laguerre, Legendre and Bessel. Those of Airy functions AiryAi and AiryBi, of stationary localised wavepacket, of polar equation of motion under the gravitational interaction, of Quantum Mechanical problem of a particle in a 1D box have also been solved. Mathematica 6.0 has been used to solve system of linear equations that we encounter and to plot numerical data. The comparison with known analytic solutions shows nearly perfect agreement in almost every case. By reading this book, readers will become adept in using finite difference method in numerically solving boundary value problems with two known derivative boundary conditions.
Sujaul Chowdhury (s.chowdhury-phy@sust.edu) is a Professor in the Department of Physics, Shahjalal University of Science and Technology (SUST) www.sust.edu, Sylhet 3114, Bangladesh. He studied Physics at SUST, did PhD in The University of Glasgow, www.gla.ac.uk, U.K. and was a Humboldt Research Fellow for one year at The Max Planck Institute, www.fkf.mpg.de, Stuttgart, Germany. Details are in https://www.sust.edu/d/phy/faculty-profile-detail/157. Abhijeet Debnath Abhi is an M.S. student of the Department of Physics, SUST. He is a promising future intellect. The work has been done by the two authors using computational facility in Nanostructure Physics Computational Lab. in the Department of Physics, SUST.
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