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Brunner, Hermann

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Author ID: brunner.hermann Recent zbMATH articles by "Brunner, Hermann"
Published as: Brunner, Hermann; Brunner, H.; Brunner, Herrmann
Homepage: http://www.math.hkbu.edu.hk/~hbrunner/
External Links: MGP · Wikidata · dblp
Documents Indexed: 174 Publications since 1967, including 7 Books
Reviewing Activity: 209 Reviews
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Serials

14 SIAM Journal on Numerical Analysis
12 IMA Journal of Numerical Analysis
12 Mathematics of Computation
12 Journal of Computational and Applied Mathematics
9 Journal of Integral Equations and Applications
8 Applied Numerical Mathematics
7 BIT
7 Computing
5 Communications on Pure and Applied Analysis
4 SIAM Journal on Scientific Computing
3 Computers & Mathematics with Applications
3 Journal of Computational Physics
3 Numerische Mathematik
3 Utilitas Mathematica
3 Journal of Scientific Computing
3 Discrete and Continuous Dynamical Systems
3 BIT. Nordisk Tidskrift for Informationsbehandling
3 Frontiers of Mathematics in China
2 Journal of the Institute of Mathematics and its Applications
2 Journal of Mathematical Analysis and Applications
2 Numerical Functional Analysis and Optimization
2 Journal of Computational Mathematics
2 Cambridge Monographs on Applied and Computational Mathematics
2 Communications in Computational Physics
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 ACM Transactions on Mathematical Software
1 Applied Mathematics and Computation
1 Calcolo
1 Mathematika
1 Ricerche di Matematica
1 Journal of Integral Equations
1 SIAM Journal on Scientific and Statistical Computing
1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII
1 Zeitschrift für Analysis und ihre Anwendungen
1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid
1 SIAM Journal on Applied Mathematics
1 Nieuw Archief voor Wiskunde. Vierde Serie
1 The Canadian Applied Mathematics Quarterly
1 The New York Journal of Mathematics
1 Methods and Applications of Analysis
1 Annals of Numerical Mathematics
1 Journal of Difference Equations and Applications
1 Proceedings of the Estonian Academy of Sciences. Physics, Mathematics
1 Computational Methods in Applied Mathematics
1 Acta Numerica
1 Fields Institute Communications

Publications by Year

Citations contained in zbMATH Open

156 Publications have been cited 3,021 times in 1,533 Documents Cited by Year
Collocation methods for Volterra integral and related functional differential equations. Zbl 1059.65122
Brunner, Hermann
533
2004
The numerical solution of Volterra equations. Zbl 0611.65092
Brunner, Hermann; van der Houwen, P. J.
279
1986
Blowup in diffusion equations: A survey. Zbl 0932.65098
Bandle, Catherine; Brunner, Hermann
120
1998
The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes. Zbl 0584.65093
Brunner, Herrmann
73
1985
The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Zbl 0941.65136
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi
67
1999
Numerical simulations of 2D fractional subdiffusion problems. Zbl 1197.65143
Brunner, Hermann; Ling, Leevan; Yamamoto, Masahiro
67
2010
Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels. Zbl 0998.65134
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi
57
2001
Nonpolynomial spline collocation for Volterra equations with weakly singular kernels. Zbl 0533.65087
Brunner, Hermann
55
1983
Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications. Zbl 1232.65047
Xiang, Shuhuang; Cho, Yeol Je; Wang, Haiyong; Brunner, Hermann
55
2011
On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods. Zbl 0702.65104
Brunner, Hermann
54
1990
Volterra integral equations. An introduction to theory and applications. Zbl 1376.45002
Brunner, Hermann
44
2017
Stability of numerical methods for Volterra integro-differential equations. Zbl 0282.65088
Brunner, H.; Lambert, J. D.
43
1974
\(hp\)-discontinuous Galerkin time-stepping for Volterra integrodifferential equations. Zbl 1116.65127
Brunner, Hermann; Schötzau, Dominik
40
2006
Spectral methods for pantograph-type differential and integral equations with multiple delays. Zbl 1396.65107
Ali, Ishtiaq; Brunner, Hermann; Tang, Tao
40
2009
The numerical solution of nonlinear Volterra integral equations of the second kind by collocation and iterated collocation methods. Zbl 0629.65144
Blom, J. G.; Brunner, H.
39
1987
A spectral method for pantograph-type delay differential equations and its convergence analysis. Zbl 1212.65308
Ali, Ishtiaq; Brunner, Hermann; Tang, Tao
38
2009
Polynomial spline collocation methods for Volterra integrodifferential equations with weakly singular kernels. Zbl 0634.65142
Brunner, Hermann
38
1986
Implicitly linear collocation methods for nonlinear Volterra equations. Zbl 0761.65103
Brunner, Hermann
37
1992
Iterated collocation methods and their discretizations for Volterra integral equations. Zbl 0575.65134
Brunner, Hermann
36
1984
High-order methods for the numerical solution of Volterra integro- differential equations. Zbl 0634.65143
Brunner, Hermann
36
1986
On the attainable order of collocation methods for pantograph integro-differential equations. Zbl 1023.65146
Muroya, Yoshiaki; Ishiwata, Emiko; Brunner, Hermann
34
2003
Geometric meshes in collocation methods for Volterra integral equations with proportional delays. Zbl 1014.65143
Brunner, Hermann; Hu, Qiya; Lin, Qun
34
2001
Runge-Kutta theory for Volterra integral equations of the second kind. Zbl 0496.65066
Brunner, Hermann; Hairer, Ernst; Nørsett, Syvert P.
34
1982
Implicit Runge-Kutta methods of optimal order for Volterra integro- differential equations. Zbl 0543.65092
Brunner, Hermann
33
1984
Mixed interpolation collocation methods for first and second order Volterra integro-differential equations with periodic solution. Zbl 0876.65090
Brunner, H.; Makroglou, A.; Miller, R. K.
27
1997
A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations. Zbl 0485.65087
Brunner, Hermann
27
1982
An \(hp\)-version discontinuous Galerkin method for integro-differential equations of parabolic type. Zbl 1230.65143
Mustapha, K.; Brunner, H.; Mustapha, H.; Schötzau, D.
26
2011
Finite element methods for optimal control problems governed by integral equations and integro-differential equations. Zbl 1076.65057
Brunner, Hermann; Yan, Ningning
25
2005
The numerical solution of two-dimensional Volterra integral equations by collocation and iterated collocation. Zbl 0665.65095
Brunner, Hermann; Kauthen, J.-P.
24
1989
The numerical solution of neutral Volterra integro-differential equations with delay arguments. Zbl 0828.65146
Brunner, Hermann
23
1994
Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind. Zbl 0442.65125
Brunner, Hermann; Nørsett, Syvert P.
23
1981
Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels. Zbl 1268.65171
Xiang, Shuhuang; Brunner, Hermann
21
2013
Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain. Zbl 1349.65272
Brunner, Hermann; Han, Houde; Yin, Dongsheng
21
2014
Iterated collocation methods for Volterra integral equations with delay arguments. Zbl 0803.65139
Brunner, Hermann
20
1994
Stability of solutions of delay functional integro-differential equations and their discretizations. Zbl 1049.65150
Brunner, Hermann; Vermiglio, Rossana
18
2003
Discontinuous Galerkin methods for delay differential equations of pantograph type. Zbl 1219.65076
Brunner, Hermann; Huang, Qiumei; Xie, Hehu
18
2010
Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays. Zbl 1396.65161
Brunner, Hermann
17
2009
Integral-algebraic equations: theory of collocation methods. I. Zbl 1280.65147
Liang, Hui; Brunner, Hermann
17
2013
On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations. Zbl 0857.65145
Brunner, Hermann; Yan, Ningning
16
1996
The approximate solution of Volterra equations with nonsmooth solutions. Zbl 0563.65077
Brunner, Hermann
16
1985
Collocation methods for nonlinear Volterra integro-differential equations with infinite delay. Zbl 0681.65105
Brunner, Hermann
16
1989
A family of methods for Abel integral equations of the second kind. Zbl 0724.65130
Brunner, H.; Crisci, M. R.; Russo, E.; Vecchio, A.
16
1991
The spectral problem for a class of highly oscillatory Fredholm integral operators. Zbl 1185.45002
Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
16
2010
Continuous collocation approximations to solutions of first kind Volterra equations. Zbl 0890.65138
Kauthen, J.-P.; Brunner, H.
15
1997
Numerical analysis of semilinear parabolic problems with blow-up solutions. Zbl 0862.65053
Bandle, C.; Brunner, H.
15
1994
Collocation methods for general Volterra functional integral equations with vanishing delays. Zbl 1239.65085
Xie, Hehu; Zhang, Ran; Brunner, Hermann
15
2011
Collocation methods for second-order Volterra integro-differential equations. Zbl 0651.65098
Aguilar, M.; Brunner, Hermann
15
1988
On mixed collocation methods for Volterra integral equations with periodic solution. Zbl 0878.65117
Brunner, H.; Makroglou, A.; Miller, R. K.
14
1997
Optimal superconvergence orders of iterated collocation solutions for Volterra integral equations with vanishing delays. Zbl 1103.65136
Brunner, Hermann; Hu, Qiya
14
2005
Superconvergence in collocation methods on quasi-graded meshes for functional differential equations with vanishing delays. Zbl 1109.65112
Bellen, A.; Brunner, H.; Maset, S.; Torelli, L.
14
2006
The numerical treatment of Volterra integro-differential equations with unbounded delay. Zbl 0687.65131
Brunner, Hermann
14
1989
On the numerical solution of nonlinear Volterra integro-differential equations. Zbl 0265.65056
Brunner, H.
14
1973
Optimal superconvergence results for delay integro-differential equations of Pantograph type. Zbl 1144.65083
Brunner, Hermann; Hu, Qiya
14
2007
Discontinuous Galerkin approximations for Volterra integral equations of the first kind. Zbl 1180.65175
Brunner, Hermann; Davies, Penny J.; Duncan, Dugald B.
14
2009
Collocation methods for third-kind vies. Zbl 1433.65345
Allaei, Sonia Seyed; Yang, Zhan-Wen; Brunner, Hermann
13
2017
Discretization of Volterra integral equations of the first kind. II. Zbl 0366.65058
Brunner, Hermann
13
1978
On \(V_0\)-stability of numerical methods for Volterra integral equations of the second kind. Zbl 0435.65103
Brunner, Hermann; Nørsett, Syvert P.; Wolkenfelt, P. H. M.
13
1980
On the discretization of differential and Volterra integral equations with variable delay. Zbl 0873.65126
Brunner, Hermann
13
1997
The approximate solution of initial-value problems for general Volterra integro-differential equations. Zbl 0631.65141
Brunner, Hermann
13
1988
Discretization of Volterra integral equations of the first kind. Zbl 0372.65052
Brunner, Hermann
12
1977
Recent advances in the numerical analysis of Volterra functional differential equations with variable delays. Zbl 1170.65103
Brunner, Hermann
12
2009
Polynomial spline collocation methods for the nonlinear Basset equation. Zbl 0687.65130
Brunner, H.; Tang, T.
12
1989
Existence, uniqueness and regularity of solutions to a class of third-kind Volterra integral equations. Zbl 1329.45001
Allaei, Sonia Seyed; Yang, Zhan-Wen; Brunner, Hermann
12
2015
Analysis of collocation solutions for a class of functional equations with vanishing delays. Zbl 1259.65205
Brunner, Hermann; Xie, Hehu; Zhang, Ran
11
2011
Blow-up behavior of Hammerstein-type Volterra integral equations. Zbl 1261.45003
Brunner, H.; Yang, Z. W.
11
2012
Volterra-type integral equations of the second kind with nonsmooth solutions: High-order methods based on collocation techniques. Zbl 0543.65091
Brunner, H.; te Riele, Herman J. J.
11
1984
On implicitly linear and iterated collocation methods for Hammerstein integral equations. Zbl 0749.65090
Brunner, Hermann
11
1991
Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods. Zbl 0944.65140
Brunner, Hermann; Lin, Yanping; Zhang, Shuhua
11
1998
A super-attainable order in collocation methods for differential equations with proportional delay. Zbl 1137.65047
Ishiwata, Emiko; Muroya, Yoshiaki; Brunner, Hermann
11
2008
The maximum principle for time-fractional diffusion equations and its application. Zbl 1333.65093
Brunner, Hermann; Han, Houde; Yin, Dongsheng
11
2015
Primary discontinuities in solutions for delay integro-differential equations. Zbl 0959.45002
Brunner, Hermann; Zhang, Wenkui
10
1999
1896–1996: One hundred years of Volterra integral equations of the first kind. Zbl 0879.45001
Brunner, Hermann
10
1997
Piecewise polynomial collocation for Volterra-type integral equations of the second kind. Zbl 0382.65065
Brunner, H.; Evans, M. D.
10
1977
Superconvergence of collocation methods for Volterra integral equations of the first kind. Zbl 0391.65055
Brunner, Hermann
10
1979
Stability of collocation methods for delay differential equations with vanishing delays. Zbl 1205.65223
Brunner, Hermann; Liang, Hui
10
2010
The numerical solution of parabolic Volterra integro-differential equations on unbounded spatial domains. Zbl 1078.65126
Han, Houde; Zhu, Liang; Brunner, Hermann; Ma, Jingtang
9
2005
Computational solution of blow-up problems for semilinear parabolic PDEs on unbounded domains. Zbl 1208.65124
Brunner, Hermann; Wu, Xiaonan; Zhang, Jiwei
9
2010
The computation of the spectra of highly oscillatory Fredholm integral operators. Zbl 1238.65123
Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
9
2011
Implicit Runge-Kutta-Nyström methods for general second-order Volterra integro differential equations. Zbl 0632.65137
Brunner, H.
9
1987
Numerical blow-up of semilinear parabolic PDEs on unbounded domains in \(\mathbb R^{2}\). Zbl 1244.65128
Zhang, Jiwei; Han, Houde; Brunner, Hermann
9
2011
The \(hp\) discontinuous Galerkin method for delay differential equations with nonlinear vanishing delay. Zbl 1276.65039
Huang, Qiumei; Xie, Hehu; Brunner, Hermann
9
2013
Collocation and continuous implicit Runge-Kutta methods for a class of delay Volterra integral equations. Zbl 0818.65134
Brunner, Hermann
8
1994
The iterative correction method for Volterra integral equations. Zbl 0854.65121
Brunner, Hermann; Lin, Qun; Yan, Ningning
8
1996
Superconvergence of discontinuous Galerkin solutions for delay differential equations of pantograph type. Zbl 1232.65102
Huang, Qiumei; Xie, Hehu; Brunner, Hermann
8
2011
A posteriori error estimates of discontinuous Galerkin methods for non-standard Volterra integro-differential equations. Zbl 1094.65135
Ma, Jingtang; Brunner, Hermann
8
2006
The solution of Volterra integral equations of the first kind by piecewise polynomials. Zbl 0271.65066
Brunner, H.
8
1973
High-order collocation methods for singular Volterra functional equations of neutral type. Zbl 1119.65121
Brunner, Hermann
8
2007
Algorithm 689: Discretized collocation and iterated collocation for nonlinear Volterra integral equations of the second kind. Zbl 0900.65382
Blom, J. G.; Brunner, H.
7
1991
Runge-Kutta time discretizations of parabolic Volterra integro- differential equations. Zbl 0832.65141
Brunner, H.; Kauthen, J.-P.; Ostermann, A.
7
1995
On the singular values and eigenvalues of the Fox-Li and related operators. Zbl 1233.47022
Böttcher, Albrecht; Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
7
2010
The application of the variation of constants formulas in the numerical analysis of integral and integro-differential equations. Zbl 0483.65034
Brunner, Hermann
7
1981
On Volterra integral operators with highly oscillatory kernels. Zbl 1278.45016
Brunner, Hermann
7
2014
Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type. Zbl 1351.65047
Huang, Qiumei; Xu, Xiuxiu; Brunner, Hermann
7
2016
The dicretization of neutral functional integro-differential equations by collocation methods. Zbl 0951.65149
Brunner, H.
6
1999
Artificial boundary conditions for parabolic Volterra integro-differential equations on unbounded two-dimensional domains. Zbl 1104.65125
Han, Houde; Zhu, Liang; Brunner, Hermann; Ma, Jingtang
6
2006
On discrete superconvergence properties of spline collocation methods for nonlinear Volterra integral equations. Zbl 0758.65083
Brunner, Hermann
6
1992
The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays. Zbl 1133.65112
Brunner, Hermann
6
2006
The convergence of collocation solutions in continuous piecewise polynomial spaces for weakly singular Volterra integral equations. Zbl 1420.65139
Liang, Hui; Brunner, Hermann
6
2019
Analysis of collocation methods for nonlinear Volterra integral equations of the third kind. Zbl 1434.65320
Song, Huiming; Yang, Zhanwen; Brunner, Hermann
6
2019
The numerical analysis of functional integral and integro-differential equations of Volterra type. Zbl 1118.65391
Brunner, Hermann
6
2004
Collocation methods for integro-differential algebraic equations with index 1. Zbl 1462.65098
Liang, Hui; Brunner, Hermann
2
2020
The fine error estimation of collocation methods on uniform meshes for weakly singular Volterra integral equations. Zbl 1456.65184
Liang, Hui; Brunner, Hermann
1
2020
The convergence of collocation solutions in continuous piecewise polynomial spaces for weakly singular Volterra integral equations. Zbl 1420.65139
Liang, Hui; Brunner, Hermann
6
2019
Analysis of collocation methods for nonlinear Volterra integral equations of the third kind. Zbl 1434.65320
Song, Huiming; Yang, Zhanwen; Brunner, Hermann
6
2019
Numerical analysis and computational solution of integro-differential equations. Zbl 1405.65165
Brunner, Hermann
1
2018
Volterra integral equations. An introduction to theory and applications. Zbl 1376.45002
Brunner, Hermann
44
2017
Collocation methods for third-kind vies. Zbl 1433.65345
Allaei, Sonia Seyed; Yang, Zhan-Wen; Brunner, Hermann
13
2017
Pauses of larval development and their consequences for stage-structured populations. Zbl 1367.92095
Brunner, Hermann; Gourley, Stephen A.; Liu, Rongsong; Xiao, Yanyu
4
2017
Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type. Zbl 1351.65047
Huang, Qiumei; Xu, Xiuxiu; Brunner, Hermann
7
2016
Analysis of collocation methods for generalized auto-convolution Volterra integral equations. Zbl 1416.65560
Zhang, Ran; Liang, Hui; Brunner, Hermann
6
2016
Integral-algebraic equations: Theory of collocation methods. II. Zbl 1347.65196
Liang, Hui; Brunner, Hermann
6
2016
On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations. Zbl 1356.65261
Liang, Hui; Brunner, Hermann
6
2016
Numerical blow-up of nonlinear parabolic integro-differential equations on unbounded domain. Zbl 1352.65651
Brunner, Hermann; Tang, Tao; Zhang, Jiwei
4
2016
Existence, uniqueness and regularity of solutions to a class of third-kind Volterra integral equations. Zbl 1329.45001
Allaei, Sonia Seyed; Yang, Zhan-Wen; Brunner, Hermann
12
2015
The maximum principle for time-fractional diffusion equations and its application. Zbl 1333.65093
Brunner, Hermann; Han, Houde; Yin, Dongsheng
11
2015
The oscillation of solutions of Volterra integral and integro-differential equations with highly oscillatory kernels. Zbl 1381.45009
Brunner, Hermann; Ma, Yunyun; Xu, Yuesheng
5
2015
Artificial boundary conditions and finite difference approximations for a time-fractional diffusion-wave equation on a two-dimensional unbounded spatial domain. Zbl 1349.65272
Brunner, Hermann; Han, Houde; Yin, Dongsheng
21
2014
On Volterra integral operators with highly oscillatory kernels. Zbl 1278.45016
Brunner, Hermann
7
2014
Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels. Zbl 1268.65171
Xiang, Shuhuang; Brunner, Hermann
21
2013
Integral-algebraic equations: theory of collocation methods. I. Zbl 1280.65147
Liang, Hui; Brunner, Hermann
17
2013
The \(hp\) discontinuous Galerkin method for delay differential equations with nonlinear vanishing delay. Zbl 1276.65039
Huang, Qiumei; Xie, Hehu; Brunner, Hermann
9
2013
Blow-up behavior of collocation solutions to Hammerstein-type Volterra integral equations. Zbl 1277.65117
Yang, Z. W.; Brunner, H.
5
2013
Blow-up behavior of Hammerstein-type delay Volterra integral equations. Zbl 1273.45001
Yang, Zhanwen; Brunner, Hermann
4
2013
Erratum to: “Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications”. Zbl 1464.65028
Xiang, Shuhuang; Cho, Yeol Je; Wang, Haiyong; Brunner, Hermann
1
2013
Blow-up behavior of Hammerstein-type Volterra integral equations. Zbl 1261.45003
Brunner, H.; Yang, Z. W.
11
2012
Collocation methods for differential equations with piecewise linear delays. Zbl 1264.65124
Liang, Hui; Brunner, Hermann
5
2012
Asymptotic stability of solutions to Volterra-renewal integral equations with space maps. Zbl 1254.45012
Annunziato, M.; Brunner, H.; Messina, E.
4
2012
Discrete superconvergence of collocation solutions for first-kind Volterra integral equations. Zbl 1259.65216
Liang, Hui; Brunner, Hermann
4
2012
Asymptotic periodicity of nonlinear discrete Volterra equations and applications. Zbl 1254.39005
Cardone, Angelamaria; Del Prete, Ida; Brunner, Hermann
2
2012
Global convergence and local superconvergence of first-kind Volterra integral equation approximations. Zbl 1252.65208
Brunner, Hermann; Davies, Penny J.; Duncan, Dugald B.
1
2012
Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications. Zbl 1232.65047
Xiang, Shuhuang; Cho, Yeol Je; Wang, Haiyong; Brunner, Hermann
55
2011
An \(hp\)-version discontinuous Galerkin method for integro-differential equations of parabolic type. Zbl 1230.65143
Mustapha, K.; Brunner, H.; Mustapha, H.; Schötzau, D.
26
2011
Collocation methods for general Volterra functional integral equations with vanishing delays. Zbl 1239.65085
Xie, Hehu; Zhang, Ran; Brunner, Hermann
15
2011
Analysis of collocation solutions for a class of functional equations with vanishing delays. Zbl 1259.65205
Brunner, Hermann; Xie, Hehu; Zhang, Ran
11
2011
The computation of the spectra of highly oscillatory Fredholm integral operators. Zbl 1238.65123
Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
9
2011
Numerical blow-up of semilinear parabolic PDEs on unbounded domains in \(\mathbb R^{2}\). Zbl 1244.65128
Zhang, Jiwei; Han, Houde; Brunner, Hermann
9
2011
Superconvergence of discontinuous Galerkin solutions for delay differential equations of pantograph type. Zbl 1232.65102
Huang, Qiumei; Xie, Hehu; Brunner, Hermann
8
2011
Numerical simulations of 2D fractional subdiffusion problems. Zbl 1197.65143
Brunner, Hermann; Ling, Leevan; Yamamoto, Masahiro
67
2010
Discontinuous Galerkin methods for delay differential equations of pantograph type. Zbl 1219.65076
Brunner, Hermann; Huang, Qiumei; Xie, Hehu
18
2010
The spectral problem for a class of highly oscillatory Fredholm integral operators. Zbl 1185.45002
Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
16
2010
Stability of collocation methods for delay differential equations with vanishing delays. Zbl 1205.65223
Brunner, Hermann; Liang, Hui
10
2010
Computational solution of blow-up problems for semilinear parabolic PDEs on unbounded domains. Zbl 1208.65124
Brunner, Hermann; Wu, Xiaonan; Zhang, Jiwei
9
2010
On the singular values and eigenvalues of the Fox-Li and related operators. Zbl 1233.47022
Böttcher, Albrecht; Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
7
2010
Time transformations for state-dependent delay differential equations. Zbl 1194.34135
Brunner, Hermann; Maset, Stefano
4
2010
Spectral methods for pantograph-type differential and integral equations with multiple delays. Zbl 1396.65107
Ali, Ishtiaq; Brunner, Hermann; Tang, Tao
40
2009
A spectral method for pantograph-type delay differential equations and its convergence analysis. Zbl 1212.65308
Ali, Ishtiaq; Brunner, Hermann; Tang, Tao
38
2009
Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays. Zbl 1396.65161
Brunner, Hermann
17
2009
Discontinuous Galerkin approximations for Volterra integral equations of the first kind. Zbl 1180.65175
Brunner, Hermann; Davies, Penny J.; Duncan, Dugald B.
14
2009
Recent advances in the numerical analysis of Volterra functional differential equations with variable delays. Zbl 1170.65103
Brunner, Hermann
12
2009
Time transformations for delay differential equations. Zbl 1187.34093
Brunner, Hermann; Maset, Stefano
3
2009
A super-attainable order in collocation methods for differential equations with proportional delay. Zbl 1137.65047
Ishiwata, Emiko; Muroya, Yoshiaki; Brunner, Hermann
11
2008
Collocation methods for pantograph-type Volterra functional equations with multiple delays. Zbl 1153.65123
Brunner, H.
3
2008
Optimal superconvergence results for delay integro-differential equations of Pantograph type. Zbl 1144.65083
Brunner, Hermann; Hu, Qiya
14
2007
High-order collocation methods for singular Volterra functional equations of neutral type. Zbl 1119.65121
Brunner, Hermann
8
2007
\(hp\)-discontinuous Galerkin time-stepping for Volterra integrodifferential equations. Zbl 1116.65127
Brunner, Hermann; Schötzau, Dominik
40
2006
Superconvergence in collocation methods on quasi-graded meshes for functional differential equations with vanishing delays. Zbl 1109.65112
Bellen, A.; Brunner, H.; Maset, S.; Torelli, L.
14
2006
A posteriori error estimates of discontinuous Galerkin methods for non-standard Volterra integro-differential equations. Zbl 1094.65135
Ma, Jingtang; Brunner, Hermann
8
2006
Artificial boundary conditions for parabolic Volterra integro-differential equations on unbounded two-dimensional domains. Zbl 1104.65125
Han, Houde; Zhu, Liang; Brunner, Hermann; Ma, Jingtang
6
2006
The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays. Zbl 1133.65112
Brunner, Hermann
6
2006
On the regularity of solutions to Volterra functional integro-differential equations with weakly singular kernels. Zbl 1147.45007
Brunner, Hermann; Ma, Jingtang
2
2006
Abstract cascading multigrid preconditioners in Besov spaces. Zbl 1133.65074
Ma, Jingtang; Brunner, Hermann
1
2006
Finite element methods for optimal control problems governed by integral equations and integro-differential equations. Zbl 1076.65057
Brunner, Hermann; Yan, Ningning
25
2005
Optimal superconvergence orders of iterated collocation solutions for Volterra integral equations with vanishing delays. Zbl 1103.65136
Brunner, Hermann; Hu, Qiya
14
2005
The numerical solution of parabolic Volterra integro-differential equations on unbounded spatial domains. Zbl 1078.65126
Han, Houde; Zhu, Liang; Brunner, Hermann; Ma, Jingtang
9
2005
Collocation methods for Volterra integral and related functional differential equations. Zbl 1059.65122
Brunner, Hermann
533
2004
The numerical analysis of functional integral and integro-differential equations of Volterra type. Zbl 1118.65391
Brunner, Hermann
6
2004
On the divergence of collocation solutions in smooth piecewise polynomial spaces for Volterra integral equations. Zbl 1079.65131
Brunner, Hermann
5
2004
The discretizaton of Volterra functional integral equations with proportional delays. Zbl 1067.65149
Brunner, Hermann
3
2004
Discretization of Volterra integral equations with weakly singular kernels. Zbl 1060.65683
Brunner, Hermann
2
2004
On the attainable order of collocation methods for pantograph integro-differential equations. Zbl 1023.65146
Muroya, Yoshiaki; Ishiwata, Emiko; Brunner, Hermann
34
2003
Stability of solutions of delay functional integro-differential equations and their discretizations. Zbl 1049.65150
Brunner, Hermann; Vermiglio, Rossana
18
2003
Time-stepping methods for Volterra-Fredholm integral equations. Zbl 1095.65117
Brunner, Hermann; Messina, Eleonora
3
2003
Continuous and discrete time waveform relaxation methods for Volterra integral equations with weakly singular kernels. Zbl 1146.65330
Brunner, H.; Crisci, M. R.; Russo, E.; Vecchio, A.
5
2002
Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels. Zbl 0998.65134
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi
57
2001
Geometric meshes in collocation methods for Volterra integral equations with proportional delays. Zbl 1014.65143
Brunner, Hermann; Hu, Qiya; Lin, Qun
34
2001
The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Zbl 0941.65136
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi
67
1999
Primary discontinuities in solutions for delay integro-differential equations. Zbl 0959.45002
Brunner, Hermann; Zhang, Wenkui
10
1999
The dicretization of neutral functional integro-differential equations by collocation methods. Zbl 0951.65149
Brunner, H.
6
1999
The use of splines in the numerical solution of differential and Volterra integral equations. Zbl 0969.65065
Brunner, Hermann
3
1999
On systems of Volterra difference equations associated with collocation methods for weakly singular Volterra integral equations. Zbl 0938.65154
Brunner, Hermann
1
1999
The numerical solution of weakly singular first-kind Volterra integral equations with delay arguments. Zbl 0967.65116
Brunner, Hermann
1
1999
Blowup in diffusion equations: A survey. Zbl 0932.65098
Bandle, Catherine; Brunner, Hermann
120
1998
Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods. Zbl 0944.65140
Brunner, Hermann; Lin, Yanping; Zhang, Shuhua
11
1998
Collocation approximations for second-order differential equations and Volterra integro-differential equations with variable delays. Zbl 0924.65140
Zhang, Wenkui; Brunner, Hermann
2
1998
On a suboptimal filtration method for solving convolution-type integral equations of the first kind. Zbl 0915.65138
Brunner, Hermann; Sizikov, Valery
1
1998
Mixed interpolation collocation methods for first and second order Volterra integro-differential equations with periodic solution. Zbl 0876.65090
Brunner, H.; Makroglou, A.; Miller, R. K.
27
1997
Continuous collocation approximations to solutions of first kind Volterra equations. Zbl 0890.65138
Kauthen, J.-P.; Brunner, H.
15
1997
On mixed collocation methods for Volterra integral equations with periodic solution. Zbl 0878.65117
Brunner, H.; Makroglou, A.; Miller, R. K.
14
1997
On the discretization of differential and Volterra integral equations with variable delay. Zbl 0873.65126
Brunner, Hermann
13
1997
1896–1996: One hundred years of Volterra integral equations of the first kind. Zbl 0879.45001
Brunner, Hermann
10
1997
On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations. Zbl 0857.65145
Brunner, Hermann; Yan, Ningning
16
1996
The iterative correction method for Volterra integral equations. Zbl 0854.65121
Brunner, Hermann; Lin, Qun; Yan, Ningning
8
1996
Open problems in the discretization of Volterra integral equations. Zbl 0882.65140
Brunner, Hermann
4
1996
Spline collocation methods for nonlinear Volterra integral equations with unknown delay. Zbl 0855.65143
Brunner, Hermann; Yatsenko, Yuri
3
1996
Runge-Kutta time discretizations of parabolic Volterra integro- differential equations. Zbl 0832.65141
Brunner, H.; Kauthen, J.-P.; Ostermann, A.
7
1995
The numerical solution of neutral Volterra integro-differential equations with delay arguments. Zbl 0828.65146
Brunner, Hermann
23
1994
Iterated collocation methods for Volterra integral equations with delay arguments. Zbl 0803.65139
Brunner, Hermann
20
1994
Numerical analysis of semilinear parabolic problems with blow-up solutions. Zbl 0862.65053
Bandle, C.; Brunner, H.
15
1994
Collocation and continuous implicit Runge-Kutta methods for a class of delay Volterra integral equations. Zbl 0818.65134
Brunner, Hermann
8
1994
Continuous Volterra-Runge-Kutta methods for integral equations with pure delay. Zbl 0782.65150
Baddour, N.; Brunner, Hermann
5
1993
...and 56 more Documents
all top 5

Cited by 1,562 Authors

72 Brunner, Hermann
26 Maleknejad, Khosrow
26 Xiang, Shuhuang
25 Vecchio, Antonia
23 Pedas, Arvet
23 Zhang, Chengjian
22 Huang, Chengming
18 Liang, Hui
16 Chen, Yanping
16 Jackiewicz, Zdzislaw
16 Vainikko, Gennadi
16 Yi, Lijun
15 Crisci, Maria Rosaria
15 Russo, Elvira
15 Wang, Wansheng
15 Zhang, Jiwei
14 Baker, Christopher T. H.
14 Conte, Dajana
14 Tamme, Enn
13 Dehghan Takht Fooladi, Mehdi
13 Diogo, Teresa
13 Ma, Jingtang
13 Tang, Tao
12 Lima, Pedro Miguel
12 Nelakanti, Gnaneshwar
12 Sezer, Mehmet
12 Sun, Zhizhong
12 Yang, Zhanwen
11 Cardone, Angelamaria
11 Ford, Neville J.
11 Kang, Hongchao
11 Li, Dongfang
11 Ma, Junjie
11 Rossi, Julio Daniel
11 Zhao, Jingjun
10 Gu, Zhendong
10 Messina, Eleonora
10 Mustapha, Kassem
10 Paternoster, Beatrice
10 Shahmorad, Sedaghat
9 Băleanu, Dumitru I.
9 Garey, Lawrence Edmund
9 Groisman, Pablo
9 Liao, HongLin
9 Stynes, Martin
9 van der Houwen, Pieter J.
9 Wang, Zhongqing
9 Xu, Zhenhua
8 Abdi, Ali
8 Cai, Haotao
8 Chen, Ruyun
8 Ding, Juntang
8 He, Guo
8 Hojjati, Gholamreza
8 Kolmanovskii, Vladimir Borisovich
8 Li, Shoufu
8 Lin, Yanping
8 Makroglou, Athena
8 Mokhtary, Payam
8 Pishbin, Saeed
8 Xu, Yang
8 Yüzbaşı, Şuayip
8 Zhang, Zhimin
7 Bulatov, Mikhail Valer’yanovich
7 Gladwin, Charles J.
7 Kauthen, Jean-Paul
7 Ling, Leevan
7 Lu, Zuliang
7 McKee, Sean
7 Payne, Lawrence Edward
7 Song, Yihong
7 Vermiglio, Rossana
7 Wen, Liping
7 Zhang, Shuhua
6 Bazm, Sohrab
6 Berenguer, María Isabel
6 D’Ambrosio, Raffaele
6 Ghoreishi, Farideh
6 Han, Guoqiang
6 Jiang, Yingjun
6 Laeli Dastjerdi, H.
6 Li, Fengjie
6 Liu, Bingchen
6 Mandal, Moumita
6 Mirzaee, Farshid
6 Ordokhani, Yadollah
6 Philippin, Gérard A.
6 Sheng, Qin
6 Shiri, Babak
6 Wang, Lina
6 Wazwaz, Abdul-Majid Abdul-Rahman
6 Wei, Yunxia
6 Xu, Da
6 Xu, Yuesheng
5 Alnasr, Modi H.
5 Assanova, Anar Turmaganbetkyzy
5 Bellen, Alfredo
5 Dehbozorgi, Raziyeh
5 Fang, Chunhua
5 Gao, Jianfang
...and 1,462 more Authors
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Cited in 219 Serials

192 Journal of Computational and Applied Mathematics
159 Applied Mathematics and Computation
121 Applied Numerical Mathematics
49 Journal of Scientific Computing
49 Journal of Integral Equations and Applications
45 Numerical Algorithms
36 Computers & Mathematics with Applications
35 International Journal of Computer Mathematics
32 BIT
32 Computational and Applied Mathematics
31 Journal of Mathematical Analysis and Applications
31 Numerische Mathematik
28 Journal of Computational Physics
26 Mathematics of Computation
25 Advances in Computational Mathematics
24 Abstract and Applied Analysis
21 SIAM Journal on Numerical Analysis
20 Computing
17 Applied Mathematical Modelling
16 Numerical Functional Analysis and Optimization
16 Frontiers of Mathematics in China
14 Advances in Difference Equations
13 Calcolo
13 SIAM Journal on Scientific Computing
12 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
12 Communications in Nonlinear Science and Numerical Simulation
12 East Asian Journal on Applied Mathematics
11 Mathematical Methods in the Applied Sciences
11 Numerical Methods for Partial Differential Equations
11 Engineering Analysis with Boundary Elements
10 Mathematical and Computer Modelling
10 Mathematical Problems in Engineering
10 Discrete and Continuous Dynamical Systems. Series B
9 Applied Mathematics Letters
9 Journal of Applied Mathematics
9 Journal of Applied Mathematics and Computing
8 Applicable Analysis
8 Mathematics and Computers in Simulation
8 Journal of Difference Equations and Applications
8 Boundary Value Problems
7 Zeitschrift für Analysis und ihre Anwendungen
7 International Journal of Applied and Computational Mathematics
6 Applications of Mathematics
6 Fractional Calculus & Applied Analysis
6 Lobachevskii Journal of Mathematics
6 Mediterranean Journal of Mathematics
5 Discrete and Continuous Dynamical Systems
5 Nonlinear Analysis. Real World Applications
5 BIT. Nordisk Tidskrift for Informationsbehandling
4 Chaos, Solitons and Fractals
4 Turkish Journal of Mathematics
4 Journal of Inequalities and Applications
4 Discrete Dynamics in Nature and Society
4 Computational Methods in Applied Mathematics
4 Asian-European Journal of Mathematics
4 Science China. Mathematics
4 Symmetry
4 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika
4 Mathematical Sciences
4 Journal of Mathematics
3 Computer Methods in Applied Mechanics and Engineering
3 Journal of the Franklin Institute
3 Linear and Multilinear Algebra
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
3 Journal of Differential Equations
3 Japan Journal of Industrial and Applied Mathematics
3 SIAM Journal on Applied Mathematics
3 Differential Equations
3 Mathematical Modelling and Analysis
3 International Journal of Computational Methods
3 Discrete and Continuous Dynamical Systems. Series S
3 Advances in Mathematical Physics
3 Nonlinear Analysis. Theory, Methods & Applications
2 Indian Journal of Pure & Applied Mathematics
2 Journal of Engineering Mathematics
2 Journal of Statistical Physics
2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
2 Aplikace Matematiky
2 Fuzzy Sets and Systems
2 Proceedings of the American Mathematical Society
2 Quarterly of Applied Mathematics
2 Scandinavian Actuarial Journal
2 Acta Applicandae Mathematicae
2 Acta Mathematicae Applicatae Sinica. English Series
2 Journal of Complexity
2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
2 Computational Mathematics and Mathematical Physics
2 Linear Algebra and its Applications
2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
2 Journal of Dynamics and Differential Equations
2 Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică
2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
2 International Journal of Nonlinear Sciences and Numerical Simulation
2 Quantitative Finance
2 Central European Journal of Mathematics
2 Mathematical Biosciences and Engineering
2 Journal of Fixed Point Theory and Applications
2 Inverse Problems and Imaging
2 Advances in Differential Equations and Control Processes
...and 119 more Serials
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Cited in 45 Fields

1,272 Numerical analysis (65-XX)
870 Integral equations (45-XX)
310 Partial differential equations (35-XX)
218 Ordinary differential equations (34-XX)
64 Real functions (26-XX)
56 Approximations and expansions (41-XX)
49 Operator theory (47-XX)
36 Probability theory and stochastic processes (60-XX)
28 Calculus of variations and optimal control; optimization (49-XX)
27 Special functions (33-XX)
27 Biology and other natural sciences (92-XX)
23 Mechanics of deformable solids (74-XX)
21 Difference and functional equations (39-XX)
17 Fluid mechanics (76-XX)
17 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
15 Harmonic analysis on Euclidean spaces (42-XX)
15 Integral transforms, operational calculus (44-XX)
12 Optics, electromagnetic theory (78-XX)
12 Statistical mechanics, structure of matter (82-XX)
11 Systems theory; control (93-XX)
10 Dynamical systems and ergodic theory (37-XX)
9 Classical thermodynamics, heat transfer (80-XX)
8 Operations research, mathematical programming (90-XX)
7 Functional analysis (46-XX)
7 Statistics (62-XX)
6 Linear and multilinear algebra; matrix theory (15-XX)
5 History and biography (01-XX)
5 Computer science (68-XX)
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2 Sequences, series, summability (40-XX)
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1 Associative rings and algebras (16-XX)
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1 Global analysis, analysis on manifolds (58-XX)
1 Quantum theory (81-XX)
1 Relativity and gravitational theory (83-XX)
1 Geophysics (86-XX)
1 Mathematics education (97-XX)

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