"The subject of this book is high order finite difference methods for time dependent PDE. The idea is to give an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the energy method and the Laplace transform. Various types of wave propagation problems are treated in specific detail since high order methods are particularly effective for these problems."--BOOK JACKET.
Series Statement
Springer series in computational mathematics, 0179-3632 ; 38
Uniform Title
Springer series in computational mathematics ; 38.
Includes bibliographical references (p. 325-330) and index.
Processing Action (note)
committed to retain
Contents
When are higher order methods effective? -- Well-posedness and stability -- Order of accuracy and convergence rate -- Approximation of space -- Approximation in time -- Coupled space-time approximations -- Boundary treatment -- The box scheme -- Wave propagation -- Problems in fluid dynamics -- Nonlinear problems with shocks -- Introduction to other numerical methods -- Appendix A: Solution of difference equations -- Appendix B: The form of SBP operators.