John P. Boyd

Bio: John P. Boyd is an academic researcher from University of Michigan. The author has contributed to research in topics: Chebyshev polynomials & Series (mathematics). The author has an hindex of 46, co-authored 282 publications receiving 10788 citations. Previous affiliations of John P. Boyd include Rutgers University & National Center for Atmospheric Research.

The Devil's Invention: Asymptotic, Superasymptotic and Hyperasymptotic Series

Abstract: Singular perturbation methods, such as the method of multiple scales and the method of matched asymptotic expansions, give series in a small parameter e which are asymptotic but (usually) divergent. In this survey, we use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a 'hyperasymptotic' approximation. This adds a second asymptotic expansion, with different scaling assumptions about the size of various terms in the problem, to achieve a minimum error much smaller than the best possible with the original asymptotic series. (This rescale-and-add process can be repeated further.) Weakly nonlocal solitary waves are used as an illustration.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

Spectral Methods in Fluid Dynamics

Abstract: Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome.

Practical Genetic Algorithms

Abstract: Introduction to Optimization The Binary Genetic Algorithm The Continuous Parameter Genetic Algorithm Applications An Added Level of Sophistication Advanced Applications Evolutionary Trends Appendix Glossary Index.