03917nam a22005775i 4500 978-3-031-69630-5 DE-He213 20251030113239.0 cr nn 008mamaa 241022s2024 sz | s |||| 0|eng d 9783031696305 978-3-031-69630-5 10.1007/978-3-031-69630-5 doi QA431 PBKJ bicssc MAT007000 bisacsh PBKJ thema Gardner, Carl L. author. aut http://id.loc.gov/vocabulary/relators/aut 86401 Applied Numerical Methods for Partial Differential Equations [electronic resource] / by Carl L. Gardner. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XXII, 216 p. 76 illus., 75 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Texts in Applied Mathematics, 2196-9949 ; 78 1 Overview -- 2 Consistency, Stability, Convergence -- 3 Numerical Methods for ODE IVPs -- 4 Numerical Methods for ODE BVPs -- 5 Overview of PDEs -- 6 Numerical Methods for Parabolic PDEs -- 7 Numerical Methods for Elliptic PDEs -- 8 Numerical Methods for Hyperbolic PDEs -- 9 Numerical Methods for Mixed Type PDEs -- A Useful Mathematical Formulas -- B Norms and Condition Number -- References -- Index . The aim of this book is to quickly elevate students to a proficiency level where they can solve linear and nonlinear partial differential equations using state-of-the-art numerical methods. It covers numerous topics typically absent in introductory texts on ODEs and PDEs, including: Computing solutions to chaotic dynamical systems with TRBDF2 Simulating the nonlinear diffusion equation with TRBDF2 Applying Newton’s method and GMRES to the nonlinear Laplace equation Analyzing gas dynamics with WENO3 (1D Riemann problems and 2D supersonic jets) Modeling the drift-diffusion equations with TRBDF2 and PCG Solving the classical hydrodynamic model (electro-gas dynamics) with WENO3 and TRBDF2 The book features 34 original MATLAB programs illustrating each numerical method and includes 93 problems that confirm results discussed in the text and explore new directions. Additionally, it suggests eight semester-long projects. This comprehensive text can serve as the basis for a one-semester graduate course on the numerical solution of partial differential equations, or, with some advanced material omitted, for a one-semester junior/senior or graduate course on the numerical solution of ordinary and partial differential equations. The topics and programs will be of interest to applied mathematicians, engineers, physicists, biologists, chemists, and more. . Difference equations. 67184 Functional equations. 67185 Mathematics Data processing. 65715 Dynamics. 65524 Nonlinear theories. 65525 Difference and Functional Equations. 67186 Computational Mathematics and Numerical Analysis. 66073 Applied Dynamical Systems. 65530 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031696299 Printed edition: 9783031696312 Printed edition: 9783031696329 Texts in Applied Mathematics, 2196-9949 ; 78 76354 https://doi.org/10.1007/978-3-031-69630-5 ZDB-2-SMA ZDB-2-SXMS 64386 64386