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Michael A. Golberg – Numerical Solution of Integral Equations
Published: 1990-06-01 | ISBN: 0306432625 | PDF | 417 pages | 14 MB

 

The principal reformulations of Laplace’s equation as boundary integral equations (BIEs) are described, together with results on their solvability and the regularity of their solutions. The numerical methods for solving BIEs are categorized, based on whether the method uses local or global approximating functions, whether the method is of collocation or Galerkin type, and whether the equation being solved is defined on a region whose boundary is smooth or only piecewise smooth. Some of the major ideas in the mathematical analysis of these numerical methods are outlined. Certain problems are associated with all numerical methods for boundary integral equations. Principal among these are numerical integration and the iterative solution of linear systems of equations. The research literature for these topics as they arise in solving BIEs is reviewed, and some of the major ideas are discussed.
This book consists of eight interesting survey papers on current topics in the numerical treatment of integral equations. Combined, these papers cover a vast area. All of them are well organized, clearly written and easy to follow. If a theorem is given without a proof, a suitable reference is supplied for the interested reader. Each paper contains a long reference list which is very useful for further study. This book also has an index, something which cannot always be taken for granted in collections of this type.

 

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