Kirjojen hintavertailu. Mukana 11 627 363 kirjaa ja 12 kauppaa.
Kirja.info

Kirjahaku

Etsi kirjoja tekijän nimen, kirjan nimen tai ISBN:n perusteella.

128 tulosta hakusanalla Royd Tolkien

Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations

Estimating the Error of Numerical Solutions of Systems of Reaction-Diffusion Equations

Donald J. Estep; Mats G. Larson; Roy D. Williams

Amer Mathematical Society
2000
pokkari
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.
Vertaile hintoja
Gas Installation Technology

Gas Installation Technology

Andrew S. Burcham; Stephen J. Denney; Roy D. Treloar

JOHN WILEY AND SONS LTD
2024
nidottu
Understand the core competencies of gas installation with this accessible textbook This fully revised third edition is an essential on-site resource and an indispensable training guide for both qualified gas engineers and new entrants to the industry. Comprehensively updated to align with the latest standards and developments, it provides unrivalled coverage of all aspects of gas installation work in the United Kingdom. This new edition features a full-colour layout, additional dedicated chapters on commercial catering, commercial laundry, educational establishments, and the ACS assessment process. With all topics consolidated into one convenient volume, gas operatives have all relevant information at their fingertips. Key Highlights: Coverage of commercial, domestic and LPG installations along with emergency service provider and meter installation details.Comprehensive index and section-numbered text for easy topic identification by trainers and learners.Detailed discussion of UK gas installation standards, practices and procedures.New and updated material on net zero targets, climate change, and other aspects of the gas industry's future. Gas Installation Technology is an invaluable training aid for students in gas installation or plumbing courses, as well as for professional gas installers renewing their certification.
Vertaile hintoja
1...567