Accuracy Verification Methods: Theory and Algorithms Softcover reprint of the original 1st ed. 2014 Edition

From the book reviews:

“An up-to-date monograph for researchers, practitioners and advanced students in scientific computing. It tries to bridge the gap between theory and practice in error estimation spanning the whole modeling and simulation process.” (A. Bultheel, Mathematical Reviews, July, 2014)

The importance of accuracy verification methods was understood at the very beginning of the development of numerical analysis. Recent decades have seen a rapid growth of results related to adaptive numerical methods and a posteriori estimates. However, in this important area there often exists a noticeable gap between mathematicians creating the theory and researchers developing applied algorithms that could be used in engineering and scientific computations for guaranteed and efficient error control.

The goals of the book are to (1) give a transparent explanation of the underlying mathematical theory in a style accessible not only to advanced numerical analysts but also to engineers and students; (2) present detailed step-by-step algorithms that follow from a theory; (3) discuss their advantages and drawbacks, areas of applicability, give recommendations and examples.