Parallel and Sequential Methods for Ordinary Differential Equations [Hardcover]

As scientific technology becomes increasingly more sophisticated, numerical analysts, mathematicians, and engineers have to solve larger and larger problems, necessitating the use of parallel computers. This book presents an up-to-date exposition of the current state of the art of numerical methods for solving ordinary equations in a parallel computing environment. Although the main focus is on problems of initial value type, boundary value problems and partial differentiation equations are also covered. Other chapters are devoted to the parallel solution of linear systems of equation, existing sequential differential equation methods, and the behavior of a parallel code based on wave relaxation.

1. Aspects of parallel computing
2. An introduction to sequential ODE methods
3. Order and stability - a general framework
4. Parallel linear algebra
5. Direct methods for ODEs
6. Diverse approaches to parallelism
7. Waveform relaxation techniques
8. Discrete waveform methods
9. Implementation of waveform algorithms
List of symbols
References

This excellent reference book is the first to attempt to survey the full range of methods for the parallel solution of ordinary differential equations....a must for all researchers in the numerical ODE community and for all scientists and engineers involved in the parallel solution of evolutionary problems modeled by differential equations. I recommend it highly. --Computing Reviews

Useful for many scientists working with large-scale problems arising after the discretization of different mathematical models as well as for numerical analysts working in the area of numerical solution of systems of ordinary differential equations. --Mathematical Reviews