Numerical Methods for Partial Differential Equations

Numerical Methods for Partial Differential Equations : Finite Difference and Finite Volume Methods

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Numerical Methods for Partial Differential Equations 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 which has been 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. * Provides a thorough understanding of how to develop computer programs for solving partial differential equations typically encountered in science and engineering from the ground up.* One of the few available resources that demonstrates the finite volume method for unstructured mesh, a method used frequently by practicing code developers in industry* Includes extensive instruction on how to solve a system of linear algebraic equations by iterative methods
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Product details

  • Hardback | 480 pages
  • 191 x 235mm
  • Academic Press Inc
  • San Diego, United States
  • English
  • 012803484X
  • 9780128034842

Review quote

"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 -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 "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
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About Sandip Mazumder

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.
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Table of contents

Introduction to Numerical Methods for Solving Differential EquationsThe Finite Difference Method (FDM)Solution to System of Linear Algebraic EquationsStability and Convergence of Iterative SolversTreatment of Time Derivative (Parabolic and Hyperbolic PDEs)The Finite Volume Method (FVM)Unstructured Finite Volume MethodMiscellaneous Topics Appendix A: Useful Relationships in Matrix Algebra Appendix B: Useful Relationships in Vector Calculus Appendix C: Tensor Notations and Useful Relationships
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