Projector-splines in the numerical solution of inetgro-differential equations

Computers and Mathematics with Applications

Volumn 35, Issue 5, 1998, Pages 107-116

  Gori, L ^a   Santi, E ^b   Cimoroni, M G ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF L'AQUILA   (Italy)

Author keywords

Cauchy principal value integral; Prandtl integral equation; Projector splines

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FUNCTIONS; INTEGRAL EQUATIONS; POLYNOMIALS; PRANDTL NUMBER;

CAUCHY PRINCIPAL VALUE INTEGRAL; CAUCHY SINGULAR INTEGRAL EQUATIONS; JACOBI WEIGHT FUNCTION; PRANDTL INTEGRAL EQUATION;

INTEGRODIFFERENTIAL EQUATIONS;

EID: 0032018963     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(98)00009-1     Document Type: Article

References (21)

1. F. Caliò, E. Marchetti and P. Rabinowitz, On the numerical solution of the generalized Prandtl equation using variation-diminishing splines, J. Comp. Appl. Math. 60 (1995), 297-307.
2. V. Demichelis, The use of modified quasi-interpolatory splines for the solution of the Prandtl equation, J. Comput. and Appl. Math. 59, 329-338 (1995).
3. L. Gori and E. Santi, A projector-splines method for solution of Cauchy singular integral equation, In Advanced Math. Tools in Metrology II, (Edited by P. Ciarlini, M.G. Cox, F. Pavese and D. Richter) Series on Adv. in Math. for Appl. Sciences, Volume 40, pp. 70-80, (1996).
4. E. Jen and R.P. Srivastav, Cubic splines and approximation solution of singular integral equations, Math. Comput. 37, 417-423 (1981).
5. A. Palamara Orsi, Spline approximation for Cauchy principal value integrals, J. Comp. Appl. Math. 30, 191-201 (1990).
6. S. Prössdorf and A. Rathsfeld, On spline Galerkin methods for singular integral equation on an interval, Num. Math. 48, 99-118 (1986).
7. P. Rabinowitz, Applications of approximating splines for the solution of Cauchy singular integral equations, Appl. Numer. Math. 15, 285-297 (1994).
8. P. Rabinowitz and E. Santi, On the uniform convergence of Cauchy principal values of quasi-interpolating splines, BIT 35, 277-290 (1995).
9. C. Dagnino and E. Santi, Quadrature rules based on projector-splines for product singular integration, Studia Univ. Babes-Bolyai, Mathematica (to appear).
10. T. Lyche and L.L. Schumaker, Local splines approximation methods, J. Approx. Theory 15, 294-325 (1975).
11. C. de Boor, On uniform approximation by splines, J. Appr. Theory 1, 219-235 (1968).
12. P. Rabinowitz, Uniform convergence results for Cauchy principal value integrals, Math. Comp. 56, 731-740 (1991).
13. C. Dagnino, V. Demichelis and E. Sante, Numerical integration based on quasi-interpolating splines, Computing 50, 149-163 (1993).
14. C. de Boor, A Practical Guide to Splines, Springer-Verlag, New York, (1978).
15. C. Dagnino, V. Demichelis and E. Santi, An algorithm for numerical integration based on quasi-interpolating splines, Numerical Algorithms 5 (1993), 443-452.
16. C. Dagnino, V. Demichelis and E. Santi, Local spline approximation methods for singular product integration, J. Appr. Theory and Its Appl. 12, 37-51 (1996).
17. C. de Boor and G.J. Fix, Spline approximations by quasi-interpolants, J. Appr. Theory 8, 19-45 (1973).
18. W. Gautschi and J. Wimp, Computing the Hubert transform of a Jacobi weight function, BIT 27, 203-215 (1987).
19. M.A. Golberg, Introduction to the numerical solution of Cauchy singular integral equations, Math. Concept and Method in Sciences and Appl., Volume 42, pp. 183-308, Plenum Press, New York, (1990).
20. N.I. Muskhelishvili, Singular Integral Equations, Noordhoff, Groningen, (1953).
21. L.L. Schumaker, Spline functions, John Wiley & Sons, New York, (1981).