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Author: Michael A. Golberg Publisher: Springer Science & Business Media ISBN: 1489925937 Category : Mathematics Languages : en Pages : 428
Book Description
In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.
Author: Grace Wahba Publisher: ISBN: Category : Languages : en Pages : 61
Book Description
The report is concerned with the numerical solution of a Fredholm integral equation of the first kind. Two methods in the literature seem to have resulted in satisfactory numerical examples. The first method is called the method of regularization of Tihonov and was studied experimentally by Tihonov and Glasko. The second method was discussed by Strand and Westwater and is called 'statistical estimation' of the solution. Both of these methods can be embedded in the general theory of the approximation of continuous linear functionals in a reproducing kernel Hilbert space. The overall purpose of this note is to demonstrate this statement in some considerable practical detail.
Author: G. Milton Wing Publisher: SIAM ISBN: 0898712637 Category : Mathematics Languages : en Pages : 141
Book Description
Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, an elementary level explanation of integral equations of the first kind.
Author: Kendall E. Atkinson
Author: Kendall E. Atkinson
Author: John T. Jefferies
Author: Kevin Ray Hickey
Author: Michael A. Golberg
Author: Mohammad Iqbal
Author: J. Wrigley
Author: Grace Wahba
Author: Jack Wrigley
Author: Bazett Annesley Lewis
Author: G. Milton Wing