An efficient and fast parallel method for Volterra integral equations of Abel type

Journal of Computational and Applied Mathematics

Volumn 189, Issue 1-2, 2006, Pages 481-493

  Capobianco, Giovanni ^a   Conte, Dajana ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

Abel equations; Chebyshev polynomial; Parallel methods; Talbot contours; Waveform relaxation methods

Indexed keywords

CHEBYSHEV APPROXIMATION; CONVERGENCE OF NUMERICAL METHODS; LAPLACE TRANSFORMS; RELAXATION PROCESSES; TIME DOMAIN ANALYSIS; WAVEFORM ANALYSIS;

ABEL EQUATIONS; CHEBYSHEV POLYNOMIALS; PARALLEL METHODS; TALBOT CONTOURS; WAVEFORM RELAXATION METHODS;

INTEGRAL EQUATIONS;

EID: 31544453874     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.03.056     Document Type: Conference Paper

References (14)

1. D.N. Arnold, and P.J. Noon Coercivity of the single layer heat potential J. Comput. Math. 7 1989 100 104
2. H. Brunner, M.R. Crisci, E. Russo, A. Vecchio, Continuous and discrete time waveform relaxation methods for Volterra integral equations with weakly singular kernels, Ricerche Mat. LI (fasc. 2) (2002) 201-222.
3. G. Capobianco, A parallel fast convergent waveform relaxation method for Volterra integral equations, Ricerche Mat. XLIX (fasc. 2) (2000) 341-352.
4. G. Capobianco, M.R. Crisci, and E. Russo Non stationary waveform relaxation methods for Abel integral equations J. Integral Equations Appl. 16 1 2004 53 66
5. E. Cuesta, Ch. Lubich, C. Palencia, Convolution quadrature time discretization of fractional diffusion-wave equations, Math. Comp. (2004), accepted for publication.
6. A. Dixon, A non linear singular Volterra integro-differential equation arising from a reaction-diffusion study of a small cell, J. Comput. Appl. Math. (1987).
7. L.A. Hageman, D.M. Young, Applied Iterative Methods, Academic Press, New York, 1981, p. 42.
8. R. Hiptmair, and A. Schädle Non-reflecting boundary conditions for Maxwell's equations Computing 71 3 2003 265 292
9. Ch. Lubich, and A. Schädle Fast convolution for non-reflecting boundary conditions SIAM J. Sci. Comput. 24 2002 161 182
10. T.A. Manteuffel The Chebyshev iteration for nonsymmetric linear systems Numer. Math. 28 1977 307 327
11. A. Nishida, Polynomial acceleration for large nonsymmetric eigenproblems, Ph.D. Thesis, 1977.
12. A. Quarteroni, R. Sacco, and F. Saleri Numerical Mathematics 2000 Springer Berlin
13. M. Rizzardi A modification of Talbot's method for the simultaneous approximation of several values of the inverse Laplace transform ACM Trans. Math. Software 21 4 1995 347 371
14. A. Talbot The accurate numerical inversion of Laplace transforms J. Inst. Math. Appl. 23 1979 97 120