search for books and compare prices
cover image
Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations
The price is the lowest for any condition, which may be new or used; other conditions may also be available. Rental copies must be returned at the end of the designated period, and may involve a deposit.
Jump down to see edition details for: Paperback
Bibliographic Detail
Publisher Amer Mathematical Society
Publication date July 1, 2000
Pages 109
Binding Paperback
Book category Adult Non-Fiction
ISBN-13 9780821820728
ISBN-10 0821820729
Dimensions 0.25 by 7.25 by 10 in.
Weight 0.50 lbs.
Original list price $52.00
Summaries and Reviews description: Product Description: This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations.Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems.We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.

Book cover for 9780821820728
The price comparison is for this edition
from Amer Mathematical Society (July 1, 2000)
9780821820728 | details & prices | 109 pages | 7.25 × 10.00 × 0.25 in. | 0.50 lbs | List price $52.00
About: This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations.

Pricing is shown for items sent to or within the U.S., excluding shipping and tax. Please consult the store to determine exact fees. No warranties are made express or implied about the accuracy, timeliness, merit, or value of the information provided. Information subject to change without notice. is not a bookseller, just an information source.