http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Numerical methods for partial differential equations
1 online resource (xiv, 365 pages) : illustrations
Front Cover; Numerical Methods for Partial Differential Equations; Copyright Page; Dedication; Table of Contents; Preface to second edition; Preface to first edition; Chapter 1. Fundamentals; 1-0 Introduction; 1-1 Classification of physical problems; 1-2 Classification of equations; 1-3 Asymptotics; 1-4 Discrete methods; 1-5 Finite differences and computational molecules; 1-6 Finite difference operators; 1 -7 Errors; 1-8 Stability and convergence; 1-9 I rregular boundaries; 1-10 Choice of discrete network; 1-11 Dimensionless forms; REFERENCES; Chapter 2. Parabolic equations; 2-0 Introduction.
2-1 Simple explicit methods2-2 Fourier stability method; 2-3 Implicit methods; 2-4 An unconditionally unstable difference equation; 2-5 Matrix stability analysis; 2-6 Extension of matrix stability analysis; 2-7 Consistency, stability, and convergence; 2-8 Pure initial value problems; 2-9 Variable coefficients; 2-10 Examples of equations with variable coefficients; 2-11 General concepts of error reduction; 2-12 Explicit methods for nonlinear problems; 2-13 An application of the explicit method; 2-14 Implicit methods for nonlinear problems; 2-15 Concluding remarks; REFERENCES.
Chapter 3. Elliptic equations3-0 Introduction; 3-1 Simple finite difference schemes; 3-2 Iterative methods; 3-3 Linear elliptic equations; 3-4 Some point iterative methods; 3-5 Convergence of point iterative methods; 3-6 Rates of convergence; 3-7 Accelerations-successive over-relaxation (SOR); 3-8 Extensions of SOR; 3-9 Qualitative examples of over-relaxation; 3-10 Other point iterative methodsf; 3-11 Block iterative methods; 3-12 Alternating direction methods; 3-13 Summary of ADI results; 3-14 Some nonlinear examples; REFERENCES; Chapter 4. Hyperbolic equations; 4-0 Introduction.
4-1 The quasilinear system4-2 Introductory examples; 4-3 Method of characteristics; 4-4 Constant states and simple waves; 4-5 Typical application of characteristics; 4-6 Explicit finite difference methods; 4-7 Overstability; 4-8 Implicit methods for second-order equations; 4-9 Nonlinear examples; 4-10 Simultaneous first-order equations-explicit methods; 4-11 An implicit method for first-order equations; 4-11 An implicit method for first-order equations; 4-13 Gas dynamics in one-space variable; 4-14 Eulerian difference equations; 4-15 Lagrangian difference equations.
4-15 Lagrangian difference equations4-16 Hopscotch methods for conservation laws; 4-17 Explicit-implicit schemes for conservation laws; REFERENCES; Chapter 5. Special topics; 5-0 Introduction; 5-1 Singularities; 5-2 Shocks; 5-3 Eigenvalue problems; 5-4 Parabolic equations in several space variables; 5-5 Additional comments on elliptic equations; 5-6 Hyperbolic equations in higher dimensions; 5-7 Mixed systems; 5-8 Higher-order equations in elasticity and vibrations; 5-9 Fluid mechanics: the Navier-Stokes equations; 5-10 Introduction to Monte Carlo methods; 5-11 Method of lines; 5-12 Fast Fourier transform and applications.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
Includes bibliographical references and indexes.
Computer science and applied mathematics