메뉴 건너뛰기




Volumn 5, Issue 2, 2006, Pages 395-413

Smoothing transformation and piecewise polynomial projection methods for weakly singular fredholm integral equations

Author keywords

Predholm integral equation; Regularisation of the solution; Smoothing transformation; Weakly singular kernel

Indexed keywords


EID: 33646374189     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2006.5.395     Document Type: Article
Times cited : (36)

References (26)
  • 1
    • 10644226323 scopus 로고
    • A modified approach to the numerical solution of linear weakly singular Volterra integral equations of the seconf kind
    • J. Abdalkhani, A modified approach to the numerical solution of linear weakly singular Volterra integral equations of the seconf kind, J. Integral Equations Appl., 5 (1993), 149-166.
    • (1993) J. Integral Equations Appl. , vol.5 , pp. 149-166
    • Abdalkhani, J.1
  • 3
    • 1142305190 scopus 로고    scopus 로고
    • A new approach to the numerical solution of weakly singular Volterra integral equations
    • P. Baratella and A. P. Orsi, A new approach to the numerical solution of weakly singular Volterra integral equations, J. Computational and Applied Mathematics, 163 (2004), 401-418.
    • (2004) J. Computational and Applied Mathematics , vol.163 , pp. 401-418
    • Baratella, P.1    Orsi, A.P.2
  • 4
    • 33646142218 scopus 로고    scopus 로고
    • Collocation methods for volterra integral and related functional equations
    • Cambridge University Press
    • H. Brunner, Collocation Methods for Volterra Integral and Related Functional Equations, Cambridge Monographs on Applied and Computational Mathematics, 15, Cambridge University Press, 2004.
    • (2004) Cambridge Monographs on Applied and Computational Mathematics , vol.15
    • Brunner, H.1
  • 5
    • 0040575075 scopus 로고    scopus 로고
    • The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
    • H. Brunner, A. Pedas and G. Vainikko, The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations, Math. Comput., 227 (1999), 1079-1095.
    • (1999) Math. Comput. , vol.227 , pp. 1079-1095
    • Brunner, H.1    Pedas, A.2    Vainikko, G.3
  • 6
    • 0035382421 scopus 로고    scopus 로고
    • Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels
    • H. Brunner, A. Pedas and G. Vainikko, Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels, SIAM J. Numer, Anal., 39 (2001), 957-982.
    • (2001) SIAM J. Numer, Anal. , vol.39 , pp. 957-982
    • Brunner, H.1    Pedas, A.2    Vainikko, G.3
  • 7
    • 0040224520 scopus 로고
    • Singularity preserving Galerkin methods for weakly singular Fredholm integral equations
    • Y. Cao and Y. Xu, Singularity preserving Galerkin methods for weakly singular Fredholm integral equations, J. Integral Equations Appl., 6 (1994), 303-334.
    • (1994) J. Integral Equations Appl. , vol.6 , pp. 303-334
    • Cao, Y.1    Xu, Y.2
  • 8
    • 84973960394 scopus 로고
    • Collocation methods for second-kind Volterra integral equations with weakly singular kernels
    • T. Diogo, S. McKee and T. Tang, Collocation methods for second-kind Volterra integral equations with weakly singular kernels, Proc. Roy. Soc. Edinburgh, 124A (1994), 199-210.
    • (1994) Proc. Roy. Soc. Edinburgh , vol.124 A , pp. 199-210
    • Diogo, T.1    McKee, S.2    Tang, T.3
  • 9
    • 0034159588 scopus 로고    scopus 로고
    • Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations, 3
    • E.A. Galperin, E.J. Kansa, A. Makroglou and S.A. Nelson, Variable transformations in the numerical solution of second kind Volterra integral equations with continuous and weakly singular kernels; extensions to Fredholm integral equations, 3. Comput. Appl. Math., 115 (2000), 93-211.
    • (2000) Comput. Appl. Math. , vol.115 , pp. 93-211
    • Galperin, E.A.1    Kansa, E.J.2    Makroglou, A.3    Nelson, S.A.4
  • 10
    • 0020012414 scopus 로고
    • Singularity expansion for the solutions of second kind Fredholm integral equations with weakly singular convolution kernels, 3
    • I.G. Graham, Singularity expansion for the solutions of second kind Fredholm integral equations with weakly singular convolution kernels, 3. Integral Equations, 4 (1982), 1-30.
    • (1982) Integral Equations , vol.4 , pp. 1-30
    • Graham, I.G.1
  • 12
    • 0040297607 scopus 로고
    • Regularity of the solution of Hammerstein equations with weakly singular kernel
    • H. Kaneko, R. Noren and Y. Xu, Regularity of the solution of Hammerstein equations with weakly singular kernel, Integral Equations Operator Theory, 13 (1990), 660-670.
    • (1990) Integral Equations Operator Theory , vol.13 , pp. 660-670
    • Kaneko, H.1    Noren, R.2    Xu, Y.3
  • 14
    • 0032381034 scopus 로고    scopus 로고
    • High order methods for weakly singular integral equations with nonsmooth input functions
    • G. Monegato and L. Scuderi, High order methods for weakly singular integral equations with nonsmooth input functions, Math. Comput., 67 (1998), 1493-1515.
    • (1998) Math. Comput. , vol.67 , pp. 1493-1515
    • Monegato, G.1    Scuderi, L.2
  • 15
    • 84976013032 scopus 로고
    • Volterra integral equations and a new Gronwall inequality, Part I: The linear case
    • J. Norbury and A.M. Stuart, Volterra integral equations and a new Gronwall inequality, Part I: The linear case, Proc. Roy. Soc. Edinburgh, 106A (1987), 361-373.
    • (1987) Proc. Roy. Soc. Edinburgh , vol.106 A , pp. 361-373
    • Norbury, J.1    Stuart, A.M.2
  • 16
    • 0013546765 scopus 로고
    • The smoothness of solutions to nonlinear weakly singular integral equations, 3
    • A. Pedas and G. Vainikko, The smoothness of solutions to nonlinear weakly singular integral equations, 3. Anal. Appl., 13 (1994), 463-476.
    • (1994) Anal. Appl. , vol.13 , pp. 463-476
    • Pedas, A.1    Vainikko, G.2
  • 17
    • 33646372942 scopus 로고    scopus 로고
    • Piecewise polynomial projection methods for nonlinear multidimensional weakly singular integral equations
    • (B. Bertram, C. Constanda, A. Struthers Eds.), Chapman&Hall/CRC, Roca-Raton-London-New York-Washington
    • A. Pedas and G. Vainikko, Piecewise polynomial projection methods for nonlinear multidimensional weakly singular integral equations, Integral Methods in Science and Engineering (B. Bertram, C. Constanda, A. Struthers Eds.), Chapman&Hall/CRC, Roca-Raton-London-New York-Washington, 2000, 280-285.
    • (2000) Integral Methods in Science and Engineering , pp. 280-285
    • Pedas, A.1    Vainikko, G.2
  • 18
    • 10644277406 scopus 로고    scopus 로고
    • Numerical solution of weakly singular Volterra integral equations with change of variables
    • A. Pedas and G. Vainikko, Numerical solution of weakly singular Volterra integral equations with change of variables, Proc. Estonian Acad. Sci. Phys. Math., 53 (2004), 99-106.
    • (2004) Proc. Estonian Acad. Sci. Phys. Math. , vol.53 , pp. 99-106
    • Pedas, A.1    Vainikko, G.2
  • 19
    • 10644255642 scopus 로고    scopus 로고
    • Smoothing transformation and collocation for weakly singular Volterra integral equations
    • A. Pedas and G. Vainikko, Smoothing transformation and collocation for weakly singular Volterra integral equations, Computing, 73 (2004), 271-293
    • (2004) Computing , vol.73 , pp. 271-293
    • Pedas, A.1    Vainikko, G.2
  • 20
    • 33646364771 scopus 로고    scopus 로고
    • Integral equations with diagonal and boundary singularities of the kernel, 3
    • to appear
    • A. Pedas and G. Vainikko, Integral equations with diagonal and boundary singularities of the kernel, 3. Anal. Appl. (to appear).
    • Anal. Appl.
    • Pedas, A.1    Vainikko, G.2
  • 21
    • 0040670110 scopus 로고
    • Regularity of the solution to a class of weakly singular Predholm integral equations of the second kind
    • C. Schneider, Regularity of the solution to a class of weakly singular Predholm integral equations of the second kind, Integral Equations and Operator Theory, 2 (1979), 62-68.
    • (1979) Integral Equations and Operator Theory , vol.2 , pp. 62-68
    • Schneider, C.1
  • 22
    • 0004408713 scopus 로고
    • Superconvergence of numerical solutions to weakly singular Volterra integro-differential equations
    • T. Tang, Superconvergence of numerical solutions to weakly singular Volterra integro-differential equations, Numer. Math., 61 (1992), 373-382.
    • (1992) Numer. Math. , vol.61 , pp. 373-382
    • Tang, T.1
  • 23
    • 1542766225 scopus 로고
    • A note collocation methods for Volterra integra-differential equations with weakly singular kernels
    • T. Tang, A note collocation methods for Volterra integra-differential equations with weakly singular kernels, IMA J. Numer. Anal., 13 (1993), 93-99.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 93-99
    • Tang, T.1
  • 25
    • 0040297593 scopus 로고
    • The properties of solutions of weakly singular integral equations, 3
    • G. Vainikko and A. Pedas, The properties of solutions of weakly singular integral equations, 3. Austral. Math. Soc. Ser B, 22 (1981), 419-430.
    • (1981) Austral. Math. Soc. Ser B , vol.22 , pp. 419-430
    • Vainikko, G.1    Pedas, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.