TAILIEUCHUNG - Partial Differential Equations part 2

engineering; these methods allow considerable freedom in putting computational elements where you want them, important when dealing with highly irregular geometries. Spectral methods [13-15] are preferred for very regular geometries and smooth functions | 834 Chapter 19. Partial Differential Equations engineering these methods allow considerable freedom in putting computational elements where you want them important when dealing with highly irregular geometries. Spectral methods 13-15 are preferred for very regular geometries and smooth functions they converge more rapidly than finite-difference methods cf. but they do not work well for problems with discontinuities. CITED REFERENCES AND FURTHER READING Ames . 1977 Numerical Methods for Partial Differential Equations 2nd ed. New York Academic Press . 1 Richtmyer . and Morton . 1967 Difference Methods forInitial Value Problems 2nd ed. New York Wiley-Interscience . 2 Roache . 1976 Computational Fluid Dynamics Albuquerque Hermosa . 3 Mitchell . and Griffiths . 1980 The Finite Difference Method in Partial Differential Equations New York Wiley includes discussion of finite element methods . 4 Dorr . 1970 SIAM Review vol. 12 pp. 248-263. 5 Meijerink . and van der Vorst . 1977 Mathematics of Computation vol. 31 pp. 148162. 6 van der Vorst . 1981 Journal of Computational Physics vol. 44 pp. 1-19 review of sparse iterative methods . 7 Kershaw . 1970 Journal of Computational Physics vol. 26 pp. 43-65. 8 Stone . 1968 SIAM Journal on Numerical Analysis vol. 5 pp. 530-558. 9 Jesshope . 1979 Computer PhysicsCommunications vol. 17 pp. 383-391. 10 Strang G. and Fix G. 1973 An Analysis of the Finite Element Method Englewood Cliffs NJ Prentice-Hall . 11 Burnett . 1987 Finite Element Analysis From Concepts to Applications Reading MA Addison-Wesley . 12 Gottlieb D. and Orszag . 1977 Numerical Analysis of Spectral Methods Theory and Applications Philadelphia . . 13 Canuto C. Hussaini . Quarteroni A. and Zang . 1988 Spectral Methods in Fluid Dynamics New York Springer-Verlag . 14 Boyd . 1989 Chebyshev andFourier SpectralMethods New York Springer-Verlag . 15 Flux-Conservative Initial Value Problems A large class of .

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