NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS USING FINITE DIFFERENCE METHOD AND MATHEMATICA

· American Academic Press
Ebook
94
Pages
Eligible

About this ebook

The book is intended for graduate students of Engineering, Mathematics and Physics. We have numerically solved Hyperbolic and Parabolic partial differential equations with various initial conditions using Finite Difference Method and Mathematica. Replacing derivatives by finite difference approximations in these differential equations in conjunction with boundary conditions and initial conditions lead to equations relating numerical solutions at various position and time. These relations are intricate in that numerical value of the solution at one particular position and time is related with that at several other position and time. We have surmounted the intricacies by writing programs in Mathematica 6.0 that neatly provide systematic tabulation of the numerical values for all necessary position and time. This enabled us to plot the solutions as functions of position and time. Comparison with analytic solutions revealed nearly perfect match in every case. We have demonstrated conditions under which the nearly perfect match can be obtained even for larger increments in position or time. 
The book is intended for graduate students of Engineering, Mathematics and Physics. We have numerically solved Hyperbolic and Parabolic partial differential equations with various initial conditions using Finite Difference Method and Mathematica. Replacing derivatives by finite difference approxi...

Discover more

About the author

Sujaul Chowdhury (s.chowdhury-phy@sust.edu) is a Professor in Department of Physics, Shahjalal University of Science and Technology (SUST) www.sust.edu, Sylhet 3114, Bangladesh. He obtained B.Sc. (Honours) in Physics in 1994 and M.Sc. in Physics in 1996 from SUST. He obtained Ph.D. in Physics from The University of Glasgow, www.gla.ac.uk U.K. in 2001. He was a Humboldt Research Fellow for one year at The Max Planck Institute, www.fkf.mpg.de, Stuttgart, Germany. Dr. Chowdhury has a glorious record of academic, scientific, teaching and research achievements; details are in http://schowdhury-phy.weebly.com. Ponkog Kumar Das (pkdas-phy@sust.edu) is an Assistant Professor in Department of Physics, SUST. He obtained B.Sc. (Honours) and M.S. in Physics from SUST. He is a promising future intellect. Details about him can be found at https://www.sust.edu/d/phy/faculty. The work has been done by the two authors using the computational facility in Nanostructure Physics Computational Lab. in Department of Physics, SUST. 

Sujaul Chowdhury (s.chowdhury-phy@sust.edu) is a Professor in Department of Physics, Shahjalal University of Science and Technology (SUST) www.sust.edu, Sylhet 3114, Bangladesh. He obtained B.Sc. (Honours) in Physics in 1994 and M.Sc. in Physics in 1996 from SUST. He obtained Ph.D. in Physics fro...

Rate this ebook

Tell us what you think.

Reading information

Smartphones and tablets
Install the Google Play Books app for Android and iPad/iPhone. It syncs automatically with your account and allows you to read online or offline wherever you are.
Laptops and computers
You can listen to audiobooks purchased on Google Play using your computer's web browser.
eReaders and other devices
To read on e-ink devices like Kobo eReaders, you'll need to download a file and transfer it to your device. Follow the detailed Help Center instructions to transfer the files to supported eReaders.