Quadrature rules for singular integrals with application to Schwarz--Christoffel mappings

Journal Article · Tue Mar 01 04:00:00 EST 1988 · J. Comput. Phys.; (United States)

DOI:https://doi.org/10.1016/0021-9991(88)90096-4· OSTI ID:5340830

Floryan, J M; Zemach, C

Numerical quadrature rules for singular integrals are presented and error bounds are derived. The rules are simple modifications of composite Newton--Cotes formulas. For singularities of type x/sup ..cap alpha../,..cap alpha..>-1, the lowest order rule (modified midpoint rule) has error terms of order ..delta../sup 2/, ..delta../sup 2//sup : //sup ..cap alpha../, and ..delta../sup 2/log (1/..delta..), where ..delta.. is the subinterval length. The rule proposed by Davis for integration of the Schwarz--Chritoffel equation for conformal mapping of polygons is shown to have error terms of the same order. For polygons with sharp corners. i.e., ..cap alpha.. close to -1, the number of integration subintervals required for the Schwarz--Christoffel equation can be reduced by several orders of magnitude by use of higher order rules given here. Explicit formulas are given for four rules of most likely utility; they are extensions of the midpoint trapezoidal, Simpson's, and 4-point rules. copyright 1988 Academic Press, Inc.

• Research Organization: Faculty of Engineering Science, The University of Western Ontario, London, Ontario, Canada N6A5B9
• OSTI ID: 5340830
• Journal Information: J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 75:1; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990230* -- Mathematics & Mathematical Models-- (1987-1989)
CONFORMAL MAPPING
ERRORS
INTEGRALS
MAPPING
QUADRATURES
SINGULARITY
TOPOLOGICAL MAPPING
TRANSFORMATIONS