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Applied Numerical Methods for Partial Differential Equations de Carl L. Gardner

Applied Numerical Methods for Partial Differential Equations: Texts in Applied Mathematics, cartea 78

Autor Carl L. Gardner
en Limba Engleză Hardback – 20 dec 2024
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.
 
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Specificații

ISBN-13: 9783031696299
ISBN-10: 3031696298
Pagini: 198
Ilustrații: Approx. 200 p. 75 illus.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.51 kg
Ediția:2025
Editura: Springer Nature Switzerland
Colecția Springer
Seria Texts in Applied Mathematics

Locul publicării:Cham, Switzerland

Cuprins

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 .

Notă biografică

Carl Gardner is an Emeritus Professor of Mathematics at Arizona State University, where he taught and did research in Computational Mathematics for 30 years.  Previously he held positions at Bowdoin College, NYU, and Duke University.Professor Gardner's research focuses on computational and theoretical fluid dynamics and the numerical solution of nonlinear partial differential equations.  His primary application areas are charge transport in quantum semiconductor devices, ion transport in biological cells (modeling ionic channels as well as synapses), and supersonic flows in astrophysical jets (modeling interactions of jets with their environments and star formation).  These problems are governed by coupled systems of nonlinear partial differential equations, and exhibit complex fluid dynamical phenomena involving nonlinear wave interactions.

Textul de pe ultima copertă

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.
 

Caracteristici

Rapidly advances students to the level where they can solve (systems of) nonlinear partial differential equations Provides model programs in MATLAB illustrating each of the numerical methods Emphasizes scientific applications, especially fluid and gas dynamics