메뉴 건너뛰기




Volumn 229, Issue 2, 2009, Pages 363-372

Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations

Author keywords

Collocation methods; Iterated collocation; Singular kernel; Volterra integral equation

Indexed keywords

COLLOCATION METHODS; CONVERGENCE PROPERTIES; EXACT SOLUTIONS; GLOBAL CONVERGENCES; HEAT CONDUCTION PROBLEMS; ITERATED COLLOCATION; NUMERICAL EXAMPLES; SINGULAR KERNEL; SPLINE COLLOCATIONS; SUPER CONVERGENCES; THEORETICAL RESULTS; VOLTERRA INTEGRAL EQUATION; WEAKLY SINGULARS;

EID: 67349138726     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.04.002     Document Type: Article
Times cited : (42)

References (22)
  • 1
    • 1142305190 scopus 로고    scopus 로고
    • A new approach to the numerical solution of weakly singular Volterra integral equations
    • Baratella P., and Orsi A.P. A new approach to the numerical solution of weakly singular Volterra integral equations. J. Comput. Appl. Math. 163 (2004) 401-418
    • (2004) J. Comput. Appl. Math. , vol.163 , pp. 401-418
    • Baratella, P.1    Orsi, A.P.2
  • 2
    • 2042437488 scopus 로고
    • On a heat conduction problem
    • Bartoshevich M.A. On a heat conduction problem. Inz ̌.- Fiz. Z ̌. 28 (1975) 340-346
    • (1975) Inz ̌.- Fiz. Z ̌. , vol.28 , pp. 340-346
    • Bartoshevich, M.A.1
  • 3
    • 84966204227 scopus 로고
    • The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes
    • Brunner H. The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes. Math. Comp. 45 (1985) 417-437
    • (1985) Math. Comp. , vol.45 , pp. 417-437
    • Brunner, H.1
  • 5
    • 0020998704 scopus 로고
    • Nonpolynomial spline collocation for Volterra equations with weakly singular kernels
    • Brunner H. Nonpolynomial spline collocation for Volterra equations with weakly singular kernels. SIAM J. Numer. Anal. 20 (1983) 1106-1119
    • (1983) SIAM J. Numer. Anal. , vol.20 , pp. 1106-1119
    • Brunner, H.1
  • 7
    • 0001676643 scopus 로고
    • Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind
    • Brunner H., and Nørsett S. Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind. Numer. Math. 36 (1981) 347-358
    • (1981) Numer. Math. , vol.36 , pp. 347-358
    • Brunner, H.1    Nørsett, S.2
  • 8
    • 0040575075 scopus 로고    scopus 로고
    • The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
    • Brunner H., Pedas A., and Vainikko G. The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Math. Comp. 68 (1999) 1079-1095
    • (1999) Math. Comp. , vol.68 , pp. 1079-1095
    • Brunner, H.1    Pedas, A.2    Vainikko, G.3
  • 9
    • 0021433038 scopus 로고
    • Volterra-type integral equations of the second kind with nonsmooth solutions: High order methods based on collocation techniques
    • Brunner H., and te Riele H.J.J. Volterra-type integral equations of the second kind with nonsmooth solutions: High order methods based on collocation techniques. J. Integral Equations 6 (1984) 187-203
    • (1984) J. Integral Equations , vol.6 , pp. 187-203
    • Brunner, H.1    te Riele, H.J.J.2
  • 10
    • 24944592037 scopus 로고    scopus 로고
    • High order product integration methods for a Volterra integral equation with logarithmic singular kernel
    • Diogo T., Franco N.B., and Lima P. High order product integration methods for a Volterra integral equation with logarithmic singular kernel. Commun. Pure Appl. Anal. 3 (2004) 217-235
    • (2004) Commun. Pure Appl. Anal. , vol.3 , pp. 217-235
    • Diogo, T.1    Franco, N.B.2    Lima, P.3
  • 11
    • 44649111253 scopus 로고    scopus 로고
    • Superconvergence properties of collocation methods for a class of weakly singular Volterra integral equations
    • in press, doi:10.1016/j.cam.2007.01.023
    • T. Diogo, P. Lima, Superconvergence properties of collocation methods for a class of weakly singular Volterra integral equations, J. Comput. Appl. Math. (in press), doi:10.1016/j.cam.2007.01.023
    • J. Comput. Appl. Math
    • Diogo, T.1    Lima, P.2
  • 12
    • 33646350537 scopus 로고    scopus 로고
    • Numerical solution of a nonlinear Abel type Volterra integral equation
    • Diogo T., Lima P., and Rebelo M. Numerical solution of a nonlinear Abel type Volterra integral equation. Commun. Pure Appl. Anal. 5 (2006) 277-288
    • (2006) Commun. Pure Appl. Anal. , vol.5 , pp. 277-288
    • Diogo, T.1    Lima, P.2    Rebelo, M.3
  • 13
    • 0008761221 scopus 로고
    • A Hermite-type collocation method for the solution of an integral equation with a certain weakly singular kernel
    • Diogo T., McKee S., and Tang T. A Hermite-type collocation method for the solution of an integral equation with a certain weakly singular kernel. IMA J. Numer. Anal. 11 (1991) 595-605
    • (1991) IMA J. Numer. Anal. , vol.11 , pp. 595-605
    • Diogo, T.1    McKee, S.2    Tang, T.3
  • 14
    • 84973960394 scopus 로고
    • Collocation methods for second-kind Volterra integral equations with weakly singular kernels
    • Diogo T., Mckee S., and Tang T. 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
  • 15
    • 0034159588 scopus 로고    scopus 로고
    • Variable transformations in the numerical solution of the second kind Volterra integral equations with continuous and weakly singular kernels; extension to Fredholm integral equations
    • Galperin E.A., Kansa E.J., Makroglou A., and Nelson S.A. Variable transformations in the numerical solution of the second kind Volterra integral equations with continuous and weakly singular kernels; extension to Fredholm integral equations. J. Comput. Appl. Math. 115 (2000) 193-211
    • (2000) J. Comput. Appl. Math. , vol.115 , pp. 193-211
    • Galperin, E.A.1    Kansa, E.J.2    Makroglou, A.3    Nelson, S.A.4
  • 17
    • 0008770803 scopus 로고
    • Existence, uniqueness and smoothness results for second-kind Volterra equations with weakly singular kernels
    • Han W. Existence, uniqueness and smoothness results for second-kind Volterra equations with weakly singular kernels. J. Integral Equations Appl. 6 (1994) 365-384
    • (1994) J. Integral Equations Appl. , vol.6 , pp. 365-384
    • Han, W.1
  • 18
    • 0031211649 scopus 로고    scopus 로고
    • An extrapolation method for a Volterra integral equation with weakly singular kernel
    • Lima P.M., and Diogo T. An extrapolation method for a Volterra integral equation with weakly singular kernel. Appl. Numer. Math. 24 (1997) 131-148
    • (1997) Appl. Numer. Math. , vol.24 , pp. 131-148
    • Lima, P.M.1    Diogo, T.2
  • 19
    • 84976013032 scopus 로고
    • Volterra integral equations and a new Gronwall inequality (Part I: The linear case)
    • Norbury J., and Stuart A.M. 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
  • 20
    • 10644255642 scopus 로고    scopus 로고
    • Smoothing transformation and piecewise polynomial collocation for weakly singular Volterra integral equations
    • Pedas A., and Vainikko G. Smoothing transformation and piecewise polynomial 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
  • 21
    • 0013586003 scopus 로고
    • Collocation methods for weakly singular second-kind Volterra integral equations with non-smooth solution
    • te Riele H.J.J. Collocation methods for weakly singular second-kind Volterra integral equations with non-smooth solution. IMA J. Numer. Anal. 2 (1982) 437-449
    • (1982) IMA J. Numer. Anal. , vol.2 , pp. 437-449
    • te Riele, H.J.J.1
  • 22
    • 1542766225 scopus 로고
    • A note on collocation methods for Volterra integro-differential equations with weakly singular kernels
    • Tang T. A note on collocation methods for Volterra integro-differential equations with weakly singular kernels. IMA J. Numer. Math. 13 (1993) 93-99
    • (1993) IMA J. Numer. Math. , vol.13 , pp. 93-99
    • Tang, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.