Computational Differential Equations / Edition 2

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This is a two volume introduction to the computational solution of differential equations using a unified approach organized around the adaptive finite element method. It presents a synthesis of mathematical modeling, analysis, and computation. The goal is to provide the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modeling in science and engineering: How can we model physical phenomena using differential equations? What are the properties of solutions of differential equations? How do we compute solutions in practice? How do we 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 authors then widen the scope to cover the basic classes of linear partial differential equations modeling elasticity, heat flow, wave propagation and convection-diffusion-absorption problems. The book concludes with a chapter on the abstract framework of the finite element method for differential equations. Volume 2, to be published in early 1997, extends the scope to nonlinear differential equations and systems of equations modeling a variety of phenomena such as reaction-diffusion, fluid flow, many-body dynamics and reaches the frontiers of research. It also addresses practical implementation issues in detail. These volumes are ideal for undergraduates studying numerical analysis or differential equations. This is a new edition of a 1988 text of 275 pages by C. Johnson.

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Editorial Reviews

From the Publisher
" excellent text...a readable, up-to-date, easily accessible, and mathematically sound introduction to finite element methods...a clear elucidation of the fundamentals of the finite element method at an elementary level." SIAM REVIEW
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Product Details

  • ISBN-13: 9780521567381
  • Publisher: Cambridge University Press
  • Publication date: 3/28/2014
  • Edition description: New Edition
  • Edition number: 2
  • Pages: 538
  • Product dimensions: 5.98 (w) x 8.98 (h) x 1.10 (d)

Table of Contents

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.

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