03502nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001000153072001700163072002300180072001600203100007800219245011100297250001800408264006900426300006600495336002600561337002600587338003600613347002400649490005100673505041000724520137101134650002602505650002602531650003402557650001402591650002402605650004102629650005402670650003102724710003402755773002602789776003602815776003602851776003602887830005102923856004602974978-3-031-69630-5DE-He21320251030113239.0cr nn 008mamaa241022s2024    sz |    s    |||| 0|eng d  a97830316963057 a10.1007/978-3-031-69630-52doi 4aQA431 7aPBKJ2bicssc 7aMAT0070002bisacsh 7aPBKJ2thema1 aGardner, Carl L.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aApplied Numerical Methods for Partial Differential Equationsh[electronic resource] /cby Carl L. Gardner.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXXII, 216 p. 76 illus., 75 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aTexts in Applied Mathematics,x2196-9949 ;v780 a1 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 .  aThe 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. . 0aDifference equations. 0aFunctional equations. 0aMathematicsxData processing. 0aDynamics. 0aNonlinear theories.14aDifference and Functional Equations.24aComputational Mathematics and Numerical Analysis.24aApplied Dynamical Systems.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303169629908iPrinted edition:z978303169631208iPrinted edition:z9783031696329 0aTexts in Applied Mathematics,x2196-9949 ;v7840uhttps://doi.org/10.1007/978-3-031-69630-5