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Numerical Methods for Partial Differential Equations
Finite Difference and Finite Volume Methods
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
Sandip Mazumder (Author)
9780128498941, Elsevier Science
Paperback, published 16 December 2015
484 pages
23.4 x 19 x 3 cm, 1 kg
"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
Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses.
1. Introduction to Numerical Methods for Solving Differential Equations2. The Finite Difference Method (FDM)3. Solution to System of Linear Algebraic Equations4. Stability and Convergence of Iterative Solvers5. Treatment of Time Derivative (Parabolic and Hyperbolic PDEs)6. The Finite Volume Method (FVM)7. Unstructured Finite Volume Method8. Miscellaneous Topics AppendixA: Useful Relationships in Matrix AlgebraB: Useful Relationships in Vector CalculusC: Tensor Notations and Useful Relationships
Subject Areas: Maths for engineers [TBJ], Technology: general issues [TB], Differential calculus & equations [PBKJ]
