论文信息 - Numerical integration based on quasi-interpolating splines

Numerical integration based on quasi-interpolating splines

In this paper product quadrature rules based on quasi-interpolating splines are proposed and convergence results are proved for bounded integrands. Convergence results are also proved for sequences of Cauchy principal value integrals of these quasiinterpolating splines. Some comparisons with other methods and numerical examples are given.ZusammenfassungDie vorliegende Arbeit behandelt auf quasiinterpolierenden Splines basierende Produktquadraturformeln und beweist Konvergenzresultate für limitierte Integranden. Konvergenzresultate mit diesen quasi-interpolierenden Splines werden auch für Cauchysche Hauptwertintegralsequenzen bewiesen. Vergleiche mit anderen Methoden und numerische Beispiele werden angegeben.

[1] Apostolos Gerasoulis,et al. Piecewise-polynomial quadratures for Cauchy singular integrals , 1986 .

[2] Catterina Dagnino,et al. Product integration of piecewise continuous integrands based on cubic splineinterpolation at equally spaced nodes , 1988 .

[3] Catterina Dagnino,et al. On the convergence of spline product quadratures for Cauchy principal value integrals , 1991 .

[4] Ayse Alaylioglu,et al. Product integration of logarithmic singular integrands based on cubic splines , 1984 .

[5] Catterina Dagnino,et al. On the evaluation of one-dimensional Cauchy principal value integrals by rules based on cubic spline interpolation , 1990, Computing.

[6] P. Rabinowitz. The convergence of interpolatory product integration rules , 1986 .

[7] Carl de Boor,et al. A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[8] P. Rabinowitz. Numerical integration based on approximating splines , 1990 .

[9] Catterina Dagnino,et al. Product integration of singular integrands based on cubic spline interpolation at equally spaced nodes , 1990 .

[10] L. Schumaker,et al. Local Spline Approximation Methods , 1975 .

[11] G. Stoyan. de Boor, C., A Practical Guide to Splines. Applied Mathematical Sciences 27. Berlin‐Heidelberg‐New York, Springer‐Verlag 1978. XXIV, 392 S., DM 32,50. US $ 17.90 , 1980 .

[12] Catterina Dagnino,et al. Spline product quadrature rules for Cauchy singular integrals , 1990 .