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Numerical solution of partial differential equations. An introduction. 2nd ed. (English) Zbl 1126.65077

Cambridge: Cambridge University Press (ISBN 0-521-60793-0/pbk). xiii, 278 p. (2005).
Publisher’s description: This is the second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition (1994; Zbl 0811.65063).
However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text brings the reader up-to-date with the latest theoretical and industrial developments.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N06 Finite difference methods for boundary value problems involving PDEs
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
35L15 Initial value problems for second-order hyperbolic equations
35J25 Boundary value problems for second-order elliptic equations
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