This book will serve as a thorough step-by-step guide for graduate students and practicing engineers on the fundamental techniques, algorithms, and coding practices required for solving PDEs using the finite difference and finite volume methods.
1. Introduction to Numerical Methods for Solving Differential Equations 2. The Finite Difference Method (FDM) 3. Solution to System of Linear Algebraic Equations 4. Stability and Convergence of Iterative Solvers 5. Treatment of Time Derivative (Parabolic and Hyperbolic PDEs) 6. The Finite Volume Method (FVM) 7. Unstructured Finite Volume Method 8. Miscellaneous Topics Appendix A: Useful Relationships in Matrix Algebra B: Useful Relationships in Vector Calculus C: Tensor Notations and Useful Relationships
Sandip Mazumder received his Ph.D. in Mechanical Engineering from Penn State University. After graduation, he joined CFD Research Corporation, where he was one of the architects and early developers of the commercial computational fluid dynamics code CFD-ACE+. In 2004, he joined the Ohio State University, where he teaches both graduate and undergraduate courses in heat and mass transfer, thermodynamics, numerical methods, and computational fluid dynamics. He is the author of over fifty journal publications, which have been cited more than one thousand times according to the ISI citation index. Dr. Mazumder is the recipient of several research and teaching awards, and is a Fellow of the American Society of Mechanical Engineers since 2011.
"All in all, this is a good book for the engineering students being patient enough to study this exciting and advanced subject of numerically solving PDEs. These students will be able to analyse their computational results, compare them for several methods and use to judge on them since not all what the computer prints or draws is useful information." --Zentralblatt MATH "The book is rich in examples and numerical results. Each chapter contains exercises. The book could be a valuable text for engineering students." --Mathematical Reviews