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Volumn 32, Issue 4, 2012, Pages 1755-1785

Analysis of collocation solutions for nonstandard Volterra integral equations

Author keywords

collocation; convergence; nonstandard Volterra integral equation; superconvergence

Indexed keywords

COLLOCATION; CONVERGENCE; CONVERGENCE AND SUPERCONVERGENCE; NUMERICAL EXPERIMENTS; PIECEWISE POLYNOMIALS; REGULARITY PROPERTIES; SUPER-CONVERGENCE; VOLTERRA INTEGRAL EQUATIONS;

EID: 84862836405     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drr038     Document Type: Article
Times cited : (14)

References (17)
  • 1
    • 0001178161 scopus 로고
    • The numerical solution of nonlinear volterra integral equations of the second kind by collocation and iterated collocation methods
    • BLOM, J. G. & BRUNNER, H. (1987) The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods. SIAM J. Sci. Stat. Comput., 8, 806-830.
    • (1987) SIAM J. Sci. Stat. Comput. , vol.8 , pp. 806-830
    • Blom, J.G.1    Brunner, H.2
  • 4
    • 0343359636 scopus 로고
    • Superconvergence in collocation and implicit runge-kutta methods for volterra-type integral equations of the second kind
    • (Workshop, Mathematical Research Institute, Oberwolfach, 1979). International Series of Numerical Mathematics, Basel: Birkhauser
    • BRUNNER, H. (1980) Superconvergence in collocation and implicit Runge-Kutta methods for Volterra-type integral equations of the second kind. Numerical Treatment of Integral Equations (Workshop, Mathematical Research Institute, Oberwolfach, 1979). International Series of Numerical Mathematics, vol. 53, pp. 54-72. Basel: Birkh;auser.
    • (1980) Numerical Treatment of Integral Equations , vol.53 , pp. 54-72
    • Brunner, H.1
  • 5
    • 0041308915 scopus 로고
    • On discrete superconvergence properties of spline collocation methods for nonlinear volterra integral equations
    • BRUNNER, H.(1992) On discrete superconvergence properties of spline collocation methods for nonlinear Volterra integral equations. J. Comput. Math., 10, 348-357.
    • (1992) J. Comput. Math. , vol.10 , pp. 348-357
    • Brunner, H.1
  • 7
    • 0030080549 scopus 로고    scopus 로고
    • On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations
    • DOI 10.1016/0377-0427(96)00012-X, PII S037704279600012X
    • BRUNNER, H. & YAN, N. (1996) On global superconvergence of iterated collocation solutions to linear secondkind Volterra integral equations. J. Comput. Appl. Math., 67, 185-189. (Pubitemid 126376425)
    • (1996) Journal of Computational and Applied Mathematics , vol.67 , Issue.1 , pp. 185-189
    • Brunner, H.1    Yan, N.2
  • 8
    • 0003814602 scopus 로고
    • Mathematics in Science and Engineering, Orlando, FL: Academic Press
    • BURTON, T. A. (1983) Volterra Integral and Differential Equations. Mathematics in Science and Engineering, vol. 167. Orlando, FL: Academic Press.
    • (1983) Volterra Integral and Differential Equations , vol.167
    • Burton, T.A.1
  • 10
    • 0030394703 scopus 로고    scopus 로고
    • Chebyshev spectral solution of nonlinear Volterra-Hammerstein integral equations
    • PII S0377042796000982
    • ELNAGAR, G. N. & KAZEMI, M. (1996) Chebyshev spectral solution of nonlinear Volterra-Hammerstein integral equations. J. Comput. Appl. Math., 76, 147-158. (Pubitemid 126379504)
    • (1996) Journal of Computational and Applied Mathematics , vol.76 , Issue.1-2 , pp. 147-158
    • Elnagar, G.N.1    Kazemi, M.2
  • 11
    • 38248999258 scopus 로고
    • Asymptotic error expansion of a collocation-type method for volterra-hammerstein integral equations
    • HAN, G. Q. (1993) Asymptotic error expansion of a collocation-type method for Volterra-Hammerstein integral equations. Appl. Numer. Math., 13, 357-369.
    • (1993) Appl. Numer. Math. , vol.13 , pp. 357-369
    • Han, G.Q.1
  • 12
    • 54249095129 scopus 로고    scopus 로고
    • Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains
    • KULIK, T. & TISDELL, C. C. (2008) Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains. Int. J. Difference Equ., 3, 103-133.
    • (2008) Int. J. Difference Equ. , vol.3 , pp. 103-133
    • Kulik, T.1    Tisdell, C.C.2
  • 13
    • 30344434341 scopus 로고    scopus 로고
    • A posteriori error estimates of discontinuous Galerkin methods for non-standard Volterra integro-differential equations
    • DOI 10.1093/imanum/dri024
    • MA, J. & BRUNNER, H. (2006) A posteriori error estimates of discontinuous Galerkin methods for non-standard Volterra integro-differential equations. IMA J. Numer. Anal., 26, 78-95. (Pubitemid 43069052)
    • (2006) IMA Journal of Numerical Analysis , vol.26 , Issue.1 SPEC. ISS. , pp. 78-95
    • Ma, J.1    Brunner, H.2
  • 14
    • 0003903042 scopus 로고
    • Mathematics Lecture Note Series. Menlo Park, CA: W. A. Benjamin
    • MILLER, R. K. (1971) Nonlinear Volterra Integral Equations. Mathematics Lecture Note Series. Menlo Park, CA: W. A. Benjamin.
    • (1971) Nonlinear Volterra Integral Equations
    • Miller, R.K.1
  • 15
    • 54249098340 scopus 로고    scopus 로고
    • Properties of solutions to nonlinear dynamic integral equations on time scales
    • PACHPATTE, D. B. (2008) Properties of solutions to nonlinear dynamic integral equations on time scales. Electron. J. Differ. Equ., 136, 1-8.
    • (2008) Electron. J. Differ. Equ. , vol.136 , pp. 1-8
    • Pachpatte, D.B.1
  • 16
    • 77957040418 scopus 로고    scopus 로고
    • On a nonstandard volterra type dynamic integral equation on time scales
    • PACHPATTE, D. B. (2009) On a nonstandard Volterra type dynamic integral equation on time scales. Electron. J. Qual. Theory Differ. Equ., 72, 1-14.
    • (2009) Electron. J. Qual. Theory Differ. Equ. , vol.72 , pp. 1-14
    • Pachpatte, D.B.1
  • 17
    • 41749103348 scopus 로고    scopus 로고
    • Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling
    • DOI 10.1016/j.na.2007.03.043, PII S0362546X07002611
    • TISDELL, C. C. & ZAIDI, A. (2008) Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modelling. Nonlinear Anal., 68, 3504-3524. (Pubitemid 351491490)
    • (2008) Nonlinear Analysis, Theory, Methods and Applications , vol.68 , Issue.11 , pp. 3504-3524
    • Tisdell, C.C.1    Zaidi, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.