Author | Meis, Theodor. author |
---|---|
Title | Numerical Solution of Partial Differential Equations [electronic resource] / by Theodor Meis, Ulrich Marcowitz |
Imprint | New York, NY : Springer New York, 1981 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5885-8 |
Descript | 556 p. online resource |
I. Initial value problems for hyperbolic and parabolic differential equations -- 1. Properly posed initial value problems -- 2. Types and characteristics -- 3. Characteristic methods for first order hyperbolic systems -- 4. Banach spaces -- 5. Stability of difference methods -- 6. Examples of stable difference methods -- 7. Inhomogeneous initial value problems -- 8. Difference methods with positivity properties -- 9. Fourier transforms of difference methods -- 10. Initial value problems in several space variables -- 11. Extrapolation methods -- II. Boundary value problems for elliptic differential equations -- 12. Properly posed boundary value problems -- 13. Difference methods -- 14. Variational methods -- 15. Hermite interpolation and its application to the Ritz method -- 16. Collocation methods and boundary integral methods -- III. Solving systems of equations -- 17. Iterative methods for solving systems of linear and nonlinear equations -- 18. Overrelaxation methods for systems of linear equations -- 19. Overrelaxation methods for systems of nonlinear equations -- 20. Band width reduction for sparse matrices -- 21. Buneman Algorithm -- 22. The Schrรถder-Trottenberg reduction method -- Appendices: Fortran programs -- Appendix 0: Introduction -- Appendix 1: Method of Massau -- Appendix 2: Total implicit difference method for solving a nonlinear parabolic differential equation -- Appendix 3: Lax-Wendroff-Richtmyer method for the case of two space variables -- Appendix 4: Difference methods with SOR for solving the Poisson equation on nonrectangular regions -- Appendix 5: Programs for band matrices -- Appendix 6: The Buneman algorithm for solving the Poisson equation