Computational Differential Equations

This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.

K. Eriksson (Author), D. Estep (Author), P. Hansbo (Author), C. Johnson (Author)

9780521567381, Cambridge University Press

Paperback, published 5 September 1996

556 pages, 20 b/w illus. 40 exercises
22.9 x 15.2 x 2.9 cm, 0.791 kg

' … delightful and illuminating …' Journal of Fluid Mechanics

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.

Subject Areas: Fluid mechanics [PHDF], Numerical analysis [PBKS]