TY - JOUR
T1 - Quadrature rules for singular integrals with application to Schwarz-Christoffel mappings
AU - Floryan, J.M
AU - Zemach, Charles
N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to lbscholars@cityu.edu.hk.
PY - 1988/3
Y1 - 1988/3
N2 - 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 xα, α > -1, the lowest order rule (modified midpoint rule) has error terms of order Δ2, Δ2+α, and Δ2 log ( 1 Δ), where Δ is the subinterval length. The rule proposed by Davis for integration of the Schwarz-Christoffel equation for conformal mapping of polygons is shown to have error terms of the same order. For polygons with sharp corners, i.e., α 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. © 1988.
AB - 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 xα, α > -1, the lowest order rule (modified midpoint rule) has error terms of order Δ2, Δ2+α, and Δ2 log ( 1 Δ), where Δ is the subinterval length. The rule proposed by Davis for integration of the Schwarz-Christoffel equation for conformal mapping of polygons is shown to have error terms of the same order. For polygons with sharp corners, i.e., α 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. © 1988.
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U2 - 10.1016/0021-9991(88)90096-4
DO - 10.1016/0021-9991(88)90096-4
M3 - 21_Publication in refereed journal
VL - 75
SP - 15
EP - 30
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
IS - 1
ER -