Buch, Englisch, 378 Seiten, CDROM, Format (B × H): 155 mm x 236 mm, Gewicht: 680 g
Reihe: Textbooks in Mathematics
Buch, Englisch, 378 Seiten, CDROM, Format (B × H): 155 mm x 236 mm, Gewicht: 680 g
Reihe: Textbooks in Mathematics
ISBN: 978-1-4200-8904-2
Verlag: PAPERBACKSHOP UK IMPORT
This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical methods, such as the high-order compact difference method and the radial basis function meshless method.
Helps Students Better Understand Numerical Methods through Use of MATLAB®The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions.
All the Material Needed for a Numerical Analysis CourseBased on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors.Students can downloadMATLABcode from www.crcpress.com,enabling them toeasily modify or improve the codes to solve their own problems.
Zielgruppe
Advanced undergraduate and graduate students in mathematics.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEs
Finite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codes
Finite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDEsNumerical examples with MATLAB codes
Finite Difference Methods for Elliptic Equations Introduction Numerical solution of linear systems Error analysis with a maximum principle Some extensions Numerical examples with MATLAB codes
High-Order Compact Difference Methods 1-D problemsHigh-dimensional problemsOther high-order compact schemes
Finite Element Methods: Basic Theory Introduction to 1-D problems Introduction to 2-D problems Abstract finite element theoryExamples of conforming finite element spaces Examples of nonconforming finite elements Finite element interpolation theory Finite element analysis of elliptic problems Finite element analysis of time-dependent problems
Finite Element Methods: Programming Finite element method mesh generation Forming finite element method equations Calculation of element matrices Assembly and implementation of boundary conditions The MATLAB code for P1 element The MATLAB code for the Q1 element
Mixed Finite Element Methods An abstract formulation Mixed methods for elliptic problemsMixed methods for the Stokes problemAn example MATLAB code for the Stokes problem Mixed methods for viscous incompressible flows
Finite Element Methods for Electromagnetics Introduction to Maxwell’s equations The time-domain finite element methodThe frequency-domain finite element methodMaxwell’s equations in dispersive media
Meshless Methods with Radial Basis Functions Introduction The radial basis functions The MFS-DRMKansa’s methodNumerical examples with MATLAB codesCoupling RBF meshless methods with DDM
Other Meshless Methods Construction of meshless shape functionsThe element-free Galerkin method The meshless local Petrov–Galerkin method
Answers to Selected ProblemsIndex
Bibliographical remarks, Exercises, and References appear at the end of each chapter.