Computational Differential Equations
Cambridge University Press
Edition: Revised ed., 9/5/1996
EAN 9780521567381, ISBN10: 0521567386
Paperback, 556 pages, 22.9 x 15.2 x 2.8 cm
Language: English
This substantial revision of the text Numerical Solution of Partial Differential Equations by the Finite Element Method by C. Johnson is a two volume introduction to the computational solution of differential equations using a unified approach organised around the adaptive finite element method. It presents a synthesis of mathematical modelling, analysis and computation. It provides the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modelling in science and engineering: How to model physical phenomena using differential equations? What are the properties of solutions of differential equations? How to compute solutions in practice? How to estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. The second volume extends the scope to nonlinear differential equations and systems of equations modelling a variety of phenomena such as reaction-diffusion, fluid flow and many-body dynamics, and reaches the frontiers of research.
Part I. Introduction
1. Introduction
2. Review of calculus in one dimension
3. Piecewise polynomial approximation in one dimension
4. Review of linear algebra
5. A first example
6. Review of numerical linear algebra
Part II. Archetypes
7. An elliptic model problem
8. A parabolic model problem
9. A hyperbolic model problem
10. An elliptic-hyperbolic model problem
11. Systems of linear ode's
12. Calculus of variations
12. Computational mathematical modelling
Part III. Problems in Several Dimensions
13. Review of calculus in several dimensions
14. Elliptic problems
15. The heat equation
16. The wave equation
17. Stationary convection-diffusion
18. Time-dependent convection-diffusion
19. Eigenvalue problems
20. Power of abstraction
Part IV. Appendix
21. History of calculus
22. Femlab.
'... the aiFe book is successfully attained, viz. to present a unified approach to computational mathematical modelling based on differential equations combining aspects of mathematics, computation and application.' G. Kirlinger, International Mathematical News