Error bounds for spline-based quadrature methods for strongly singular integrals

Journal of Computational and Applied Mathematics

Volumn 89, Issue 2, 1998, Pages 257-261

  Diethelm, Kai ^a  

^a UNIVERSITY OF HILDESHEIM   (Germany)

Author keywords

Cauchy principal value integral; Hadamard finite part integral; Nodal spline; Not a knot condition; Quasi interpolatory spline; Spline approximation

Indexed keywords

INTEGRAL EQUATIONS; INTERPOLATION;

CAUCHY PRINCIPAL VALUE INTEGRALS; HADAMARD FINITE PART INTEGRALS; NODAL SPLINES; SPLINE APPROXIMATIONS;

APPROXIMATION THEORY;

EID: 0032026182     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(97)00245-8     Document Type: Article

References (17)

1. H. Brass, Zur Konstruktion fast-optimaler Algorithmen der Numerik, Abh. Braunschweig. Wiss. Ges. 46 (1995) 71-78.
2. C. Dagnino, V. Demichelis, E. Santi, Numerical integration rules based on quasi-interpolating splines, Computing 50 (1993) 149-163.
3. P.J. Davis, P. Rabinowitz, Methods of Numerical Integration, 2nd ed. Academic Press, Orlando, 1984.
4. V. Demichelis, Convergence of derivatives of optimal nodal splines, J. Approx. Theory 88 (1997) 370-383.
5. J.M. de Villiers, C. Rohwer, Optimal local spline interpolants, J. Comput. Appl. Math. 18 (1987) 107-119.
6. K. Diethelm, Uniform convergence of optimal order quadrature rules for Cauchy principal value integrals, J. Comput. Appl. Math. 56 (1994) 321-329.
7. K. Diethelm, An algorithm for the numerical solution of differential equations of fractional order, Elec. Trans. Numer. Anal. 5 (1997) 1-6.
8. K. Diethelm, Generalized compound quadrature formulae for finite-part integrals, IMA J. Numer. Anal. 17 (1997) 479-493.
9. M. Diligenti, G. Monegato, Finite-part integrals: their occurrence and computation, Rend. Circ. Mat. Palermo (2) Suppl. 33 (1993) 39-61.
10. D. Elliott, An asymptotic analysis of two algorithms for certain Hadamard finite-part integrals, IMA J. Numer. Anal. 13 (1993) 445-462.
11. T. Lyche, L.L. Schumaker, Local spline approximation methods, J. Approx. Theory 15 (1975) 294-325.
12. G. Mastroianni, Uniform convergence of derivatives of Lagrange interpolation, J. Comput. Appl. Math. 43 (1992) 37-51.
13. G. Monegato, Numerical evaluation of hypersingular integrals, J. Comput. Appl. Math. 50 (1994) 9-31.
14. K.B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, 1974.
15. A. Palamara Orsi, Spline approximation for Cauchy principal value integrals, J. Comput. Appl. Math. 30 (1990) 191-201.
16. A. Palamara Orsi, A note on spline approximation for Hadamard finite-part integrals, J. Comput. Appl. Math. 79 (1997) 67-73.
17. H.W. Stolle, R. Strauss, On the numerical integration of certain singular integrals, Computing 48 (1992) 177-189.