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

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 industryIncludes extensive instruction on how to solve a system of linear algebraic equations by iterative methods INDICE: 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

• ISBN: 978-0-12-803484-2
• Editorial: Academic Press
• Encuadernacion: Cartoné
• Páginas: 480
• Fecha Publicación: 01/12/2015
• Nº Volúmenes: 1
• Idioma: Inglés