메뉴 건너뛰기




Volumn 43, Issue 5, 2005, Pages 2144-2171

Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in Banach spaces

Author keywords

Exponentially convergent algorithms; Inhomogeneous evolution equation; Operator exponential; Sine methods

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; INITIAL VALUE PROBLEMS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS;

EID: 33749034221     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/040611045     Document Type: Article
Times cited : (44)

References (42)
  • 2
    • 33750165194 scopus 로고
    • Representation and approximation of the solution of an initial value problem for a first order differential equation with an unbounded operator coefficient in Hilbert space based on the Cayley transform
    • Progress in Partial Differential Equations, C. Bandle et al., eds., C. Bandle et al., eds., Pitman, Boston
    • D. Z. AROV, I. P. GAVRILYUK, AND V. L. MAKAROV, Representation and approximation of the solution of an initial value problem for a first order differential equation with an unbounded operator coefficient in Hilbert space based on the Cayley transform, in Progress in Partial Differential Equations, C. Bandle et al., eds., Pitman Res. Notes Math. Sci. 1, C. Bandle et al., eds., Pitman, Boston, 1994, pp. 40-50.
    • (1994) Pitman Res. Notes Math. Sci. , vol.1 , pp. 40-50
    • Arov, D.Z.1    Gavrilyuk, I.P.2    Makarov, V.L.3
  • 4
    • 33750162427 scopus 로고
    • Stability estimates for a general discretization method
    • N. YU. BAKAEV, Stability estimates for a general discretization method, Soviet Math. Dokl., 40 (1990), pp. 11-15.
    • (1990) Soviet Math. Dokl. , vol.40 , pp. 11-15
    • Bakaev, N.Yu.1
  • 5
    • 0042333263 scopus 로고    scopus 로고
    • Maximum norm resolvent estimates for elliptic finite element operators
    • N. YU. BAKAEV, Maximum norm resolvent estimates for elliptic finite element operators, BIT, 41 (2001), pp. 215-239.
    • (2001) BIT , vol.41 , pp. 215-239
    • Bakaev, N.Yu.1
  • 6
    • 0032296181 scopus 로고    scopus 로고
    • Long time behaviour of backward difference type methods for parabolic equations with memory in Banach space
    • N. YU. BAKAEV, S. LARSSON, AND V. THOMÉE, Long time behaviour of backward difference type methods for parabolic equations with memory in Banach space, Numer. Math., 6 (1998), pp. 185-206.
    • (1998) Numer. Math. , vol.6 , pp. 185-206
    • Bakaev, N.Yu.1    Larsson, S.2    Thomée, V.3
  • 7
    • 0036790312 scopus 로고    scopus 로고
    • Long time stability of variable stepsize approximations of semigroups
    • N. YU. BAKAEV AND A. OSTERMANN, Long time stability of variable stepsize approximations of semigroups, Math. Comp., 71 (2002), pp. 1575-1567.
    • (2002) Math. Comp. , vol.71 , pp. 1575-11567
    • Bakaev, N.Yu.1    Ostermann, A.2
  • 8
    • 0038584388 scopus 로고
    • Über die asymptotische Verteilung der eigenwerte partieller differentialgleichungen
    • T. CARLEMAN, Über die asymptotische Verteilung der eigenwerte partieller differentialgleichungen, Ber. der Sächs. Akad. Wiss. Leipzig, Math.-Nat. Kl., 88 (1936), pp. 119-132.
    • (1936) Ber. der Sächs. Akad. Wiss. Leipzig, Math.-nat. Kl. , vol.88 , pp. 119-132
    • Carleman, T.1
  • 9
    • 0001853829 scopus 로고
    • The stability of rational approximations of analytic semigroups
    • M. CROUZEIX, S. LARSSON, S. PISKAREV, AND V. THOMÉE, The stability of rational approximations of analytic semigroups, BIT, 33 (1993), pp. 74-84.
    • (1993) BIT , vol.33 , pp. 74-84
    • Crouzeix, M.1    Larsson, S.2    Piskarev, S.3    Thomée, V.4
  • 11
    • 0001094238 scopus 로고    scopus 로고
    • Strongly P-positive operators and explicit representation of the solutions of initial value problems for second order differential equations in Banach space
    • I. P. GAVRILYUK, Strongly P-positive operators and explicit representation of the solutions of initial value problems for second order differential equations in Banach space, J. Math. Anal. Appl., 236 (1999), pp. 327-349.
    • (1999) J. Math. Anal. Appl. , vol.236 , pp. 327-349
    • Gavrilyuk, I.P.1
  • 12
    • 0036022621 scopus 로고    scopus 로고
    • H-matrix approximation for the operator exponential with applications
    • I. P. GAVRILYUK, W. HACKBUSCH, AND B. N. KHOROMSKIJ, H-matrix approximation for the operator exponential with applications, Numer. Math., 92 (2002), pp. 83-111.
    • (2002) Numer. Math. , vol.92 , pp. 83-111
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 13
    • 2942644816 scopus 로고    scopus 로고
    • Data-sparse approximation to the operator-valued functions of elliptic operator
    • I. P. GAVRILYUK, W. HACKBUSCH, AND B. N. KHOROMSKIJ, Data-sparse approximation to the operator-valued functions of elliptic operator, Math. Comp., 73 (2004), pp. 1297-1324.
    • (2004) Math. Comp. , vol.73 , pp. 1297-1324
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 14
    • 17144410769 scopus 로고    scopus 로고
    • Tensor-product approximation to elliptic and parabolic solution operators in higher dimensions
    • I. P. GAVRILYUK, W. HACKBUSCH, AND B. N. KHOROMSKIJ, Tensor-product approximation to elliptic and parabolic solution operators in higher dimensions, Computing, 74 (2005), pp. 131-157.
    • (2005) Computing , vol.74 , pp. 131-157
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 15
    • 14944359407 scopus 로고    scopus 로고
    • Data-sparse approximation of a class of operator-valued functions
    • I. P. GAVRILYUK, W. HACKBUSCH, AND B. N. KHOROMSKIJ, Data-sparse approximation of a class of operator-valued functions, Math. Comp., 74 (2005), pp. 681-708.
    • (2005) Math. Comp. , vol.74 , pp. 681-708
    • Gavrilyuk, I.P.1    Hackbusch, W.2    Khoromskij, B.N.3
  • 16
    • 0042113929 scopus 로고
    • The Cayley transform and the solution of an initial value problem for a first order differential equation with an unbounded operator coefficient in Hilbert space
    • I. P. GAVRILYUK AND V. L. MAKAROV, The Cayley transform and the solution of an initial value problem for a first order differential equation with an unbounded operator coefficient in Hilbert space, Numer. Funct. Anal. Opt im., 15 (1994), pp. 583-598.
    • (1994) Numer. Funct. Anal. Opt Im. , vol.15 , pp. 583-598
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 17
    • 21344446470 scopus 로고    scopus 로고
    • Representation and approximation of the solution of an initial value problem for a first order differential equation in Banach space
    • I. P. GAVRILYUK AND V. L. MAKAROV, Representation and approximation of the solution of an initial value problem for a first order differential equation in Banach space, Z. Anal. Anwendungen, 15 (1996), pp. 495-527.
    • (1996) Z. Anal. Anwendungen , vol.15 , pp. 495-527
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 18
    • 85009773228 scopus 로고    scopus 로고
    • Exponentially convergent parallel discretization methods for the first order evolution equations
    • I. P. GAVRILYUK AND V. L. MAKAROV, Exponentially convergent parallel discretization methods for the first order evolution equations, Comput. Methods Appl. Math., 1 (2001), pp. 333-355.
    • (2001) Comput. Methods Appl. Math. , vol.1 , pp. 333-355
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 19
    • 33750156255 scopus 로고    scopus 로고
    • Exponentially convergent parallel discretization methods for the first order differential equations
    • I. P. GAVRILYUK AND V. L. MAKAROV, Exponentially convergent parallel discretization methods for the first order differential equations, Dokl. Ukrainian Acad. Sci., (2002), pp. 1-6.
    • (2002) Dokl. Ukrainian Acad. Sci. , pp. 1-6
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 20
    • 33750154383 scopus 로고    scopus 로고
    • Exponentially convergent algorithms for the operator exponential with applications to inhomogeneous problems in banach spaces
    • I. P. GAVRILYUK AND V. L. MAKAROV, Exponentially Convergent Algorithms for the Operator Exponential with Applications to Inhomogeneous Problems in Banach Spaces, Jenaer Schriften zur Mathematik und Informatik, FSU Jena, 4 (2004), pp. 1-34 (available online at http://www.minet.uni-jena.de/Math-Net/ reports/).
    • (2004) Jenaer Schriften zur Mathematik und Informatik, FSU Jena , vol.4 , pp. 1-34
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 21
    • 14944374194 scopus 로고    scopus 로고
    • Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces
    • I. P. GAVRILYUK AND V. L. MAKAROV, Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces, Math. Comp., 74 (2005), pp. 555-583.
    • (2005) Math. Comp. , vol.74 , pp. 555-583
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 22
    • 0004603920 scopus 로고    scopus 로고
    • An explicit boundary integral representation of the solution of the two-dimensional heat equation and its discretization
    • I. P. GAVRILYUK AND V. L. MAKAROV, An explicit boundary integral representation of the solution of the two-dimensional heat equation and its discretization, J. Integral Equations Appl., 12 (2000), pp. 63-83.
    • (2000) J. Integral Equations Appl. , vol.12 , pp. 63-83
    • Gavrilyuk, I.P.1    Makarov, V.L.2
  • 23
    • 85009797196 scopus 로고    scopus 로고
    • A new estimate of the sinc method for linear parabolic problems including the initial point
    • I. P. GAVRILYUK, V. L. MAKAROV, AND V. VASYLYK, A new estimate of the sinc method for linear parabolic problems including the initial point, Comput. Methods Appl. Math., 4 (2004), pp. 1-27.
    • (2004) Comput. Methods Appl. Math. , vol.4 , pp. 1-27
    • Gavrilyuk, I.P.1    Makarov, V.L.2    Vasylyk, V.3
  • 24
    • 0009084553 scopus 로고    scopus 로고
    • Stability of time-stepping methods for abstract time-dependent parabolic problems
    • C. GONZÁLEZ AND C. PALENCIA, Stability of time-stepping methods for abstract time-dependent parabolic problems, SIAM J. Numer. Anal., 35 (1998), pp. 973-989.
    • (1998) SIAM J. Numer. Anal. , vol.35 , pp. 973-989
    • González, C.1    Palencia, C.2
  • 25
    • 0039756624 scopus 로고    scopus 로고
    • Stability of Runge-Kutta methods for abstract time-dependent parabolic problems: The Hölder case
    • C. GONZALEZ AND C. PALENCIA, Stability of Runge-Kutta methods for abstract time-dependent parabolic problems: The Hölder case, Math. Comp., 68 (1996), pp. 73-89.
    • (1996) Math. Comp. , vol.68 , pp. 73-89
    • Gonzalez, C.1    Palencia, C.2
  • 26
    • 33750198578 scopus 로고    scopus 로고
    • Approximation of abstract differential equations
    • Moscow State University, Moscow, and http://www.srcc.msu.su/nivc/english/ about/home_pages/piskarev/obzlen.pdf
    • D. GUIDETTI, B. KARASOZEN, AND S. I. PISKAREV, Approximation of Abstract Differential Equations, Technical report, Moscow State University, Moscow, 2003; also available at http://malserv.mathematik.uni-karlsruhe.de/evolve-l/index. html and http://www.srcc.msu.su/nivc/english/about/home_pages/piskarev/obzlen. pdf.
    • (2003) Technical Report
    • Guidetti, D.1    Karasozen, B.2    Piskarev, S.I.3
  • 27
    • 0038776015 scopus 로고
    • Fractional powers of operators acting in Banach spaces
    • in Russian
    • M. A. KRASNOSEL'SKIJ AND P. E. SOBOLEVSKIJ, fractional powers of operators acting in Banach spaces, Dokl. Akad. Nauk, 129 (1959), pp. 499-502 (in Russian).
    • (1959) Dokl. Akad. Nauk , vol.129 , pp. 499-502
    • Krasnosel'skij, M.A.1    Sobolevskij, P.E.2
  • 28
    • 0000957952 scopus 로고    scopus 로고
    • Maximum norm analysis of completely discrete finite element methods for parabolic problems
    • C. PALENCIA, Maximum norm analysis of completely discrete finite element methods for parabolic problems, SIAM J. Numer. Anal., 33 (1996), pp. 1654-1668.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1654-1668
    • Palencia, C.1
  • 30
    • 0012229527 scopus 로고
    • Error estimates in the approximation of semigroups of operators by Padé fractions
    • in Russian
    • S. I. PISKAREV, Error estimates in the approximation of semigroups of operators by Padé fractions, Izv. Vyssh. Uchebn. Zaved. Mat., 4 (1979), pp. 33-38 (in Russian).
    • (1979) Izv. Vyssh. Uchebn. Zaved. Mat. , vol.4 , pp. 33-38
    • Piskarev, S.I.1
  • 31
    • 0042884422 scopus 로고    scopus 로고
    • Stability and regularization of three-level difference schemes with unbounded operator coefficients in Banach spaces
    • A. A. SAMARSKII, I. P. GAVRILYUK, AND V. L. MAKAHOV, Stability and regularization of three-level difference schemes with unbounded operator coefficients in Banach spaces, SIAM J. Numer. Anal., 39 (2001), pp. 708-723.
    • (2001) SIAM J. Numer. Anal. , vol.39 , pp. 708-723
    • Samarskii, A.A.1    Gavrilyuk, I.P.2    Makahov, V.L.3
  • 32
    • 0032358996 scopus 로고    scopus 로고
    • Stability, analyticity and almost best approximation in maximum norm for parabolic finite element equations
    • A. H. SCHATZ, V. THOMÉE, AND L. B. WAHLBIN, Stability, analyticity and almost best approximation in maximum norm for parabolic finite element equations, Comm. Pure Appl. Math., 51 (1998), pp. 1349-1385.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 1349-1385
    • Schatz, A.H.1    Thomée, V.2    Wahlbin, L.B.3
  • 33
    • 0034407089 scopus 로고    scopus 로고
    • A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature
    • D. SHEEN, I. H. SLOAN, AND V. THOMÉE, A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature, Math. Comp., 69 (2000), pp. 177-195.
    • (2000) Math. Comp. , vol.69 , pp. 177-195
    • Sheen, D.1    Sloan, I.H.2    Thomée, V.3
  • 34
    • 0345016412 scopus 로고    scopus 로고
    • A parallel method for time-discretization of parabolic equations based on Laplace transformation and quadrature
    • D. SHEEN, I. H. SLOAN, AND V. THOMÉE, A parallel method for time-discretization of parabolic equations based on Laplace transformation and quadrature, IMA J. Numer. Anal., 23 (2003), pp. 269-299.
    • (2003) IMA J. Numer. Anal. , vol.23 , pp. 269-299
    • Sheen, D.1    Sloan, I.H.2    Thomée, V.3
  • 35
    • 0347429939 scopus 로고
    • Application of the semi-group theory to investigation of differential equations in Banach spaces
    • in Russian
    • M. Z. SOLOMJAK, Application of the semi-group theory to investigation of differential equations in Banach spaces, Dokl. Akad. Nauk, 122 (1958), pp. 766-769 (in Russian).
    • (1958) Dokl. Akad. Nauk , vol.122 , pp. 766-769
    • Solomjak, M.Z.1
  • 37
    • 84968480558 scopus 로고
    • Collocating convolutions
    • F. STENGER, Collocating convolutions. Math. Comp., 64 (1995), pp. 211-235.
    • (1995) Math. Comp. , vol.64 , pp. 211-235
    • Stenger, F.1
  • 42
    • 33750176808 scopus 로고    scopus 로고
    • Uniform exponentially convergent method for the first order evolution equation with unbounded operator coefficient
    • in Russian
    • V. VASYLYK, Uniform exponentially convergent method for the first order evolution equation with unbounded operator coefficient, J. Numer. Appl. Math., 1 (2003), pp. 99-104 (in Russian).
    • (2003) J. Numer. Appl. Math. , vol.1 , pp. 99-104
    • Vasylyk, V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.