Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods (Complete Instructor's Resources with Solution Manual) (Solutions)

__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. * Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry * Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes * Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives Content: Front matter,Copyright,Dedication,About the Author,Preface,List of SymbolsEntitled to full textChapter 1 - Introduction to Numerical Methods for Solving Differential Equations, Pages 1-49 Chapter 2 - The Finite Difference Method, Pages 51-101 Chapter 3 - Solution to a System of Linear Algebraic Equations, Pages 103-167 Chapter 4 - Stability and Convergence of Iterative Solvers, Pages 169-218 Chapter 5 - Treatment of the Time Derivative (Parabolic and Hyperbolic PDEs), Pages 219-275 Chapter 6 - The Finite Volume Method (FVM), Pages 277-338 Chapter 7 - Unstructured Finite Volume Method, Pages 339-388 Chapter 8 - Miscellaneous Topics, Pages 389-441 Appendix A - Useful Relationships in Matrix Algebra, Pages 443-446 Appendix B - Useful Relationships in Vector Calculus, Pages 447-449 Appendix C - Tensor Notations and Useful Relationships, Pages 451-453 Index, Pages 455-461