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## Brunner, Hermann

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 Author ID: brunner.hermann Published as: Brunner, H.; Brunner, Hermann; 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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#### Co-Authors

 76 single-authored 10 Liang, Hui 6 Han, Houde 6 Nørsett, Syvert Paul 6 Yang, Zhanwen 5 Ma, Jingtang 5 Xie, Hehu 4 Huang, Qiumei 4 Tang, Tao 4 Zhang, Jiwei 3 Hu, Qiya 3 Iserles, Arieh 3 Kauthen, Jean-Paul 3 Maset, Stefano 3 Xiang, Shuhuang 3 Yan, Ningning 3 Zhang, Ran 2 Ali, Ishtiaq 2 Allaei, Sonia Seyed 2 Bandle, Catherine 2 Blom, Joke G. 2 Cho, Yeol Je 2 Crisci, Maria Rosaria 2 Davies, Penny J. 2 Duncan, Dugald B. 2 Ishiwata, Emiko 2 Lin, Qun 2 Makroglou, Athena 2 Messina, Eleonora 2 Miller, Richard K. 2 Muroya, Yoshiaki 2 Pedas, Arvet 2 Russo, Elvira 2 Schötzau, Dominik 2 te Riele, Herman 2 Vainikko, Gennadi M. 2 Vecchio, Antonia 2 Wang, Haiyong 2 Wu, Xiaonan 2 Yin, Dongsheng 2 Zhang, Wenkui 2 Zhu, Liang 1 Aguilar, Mónica 1 Annunziato, Mario 1 Baddour, Natalie 1 Bellen, Alfredo 1 Böttcher, Albrecht 1 Budd, Christopher John 1 Cardone, Angelamaria 1 Del Prete, Ida 1 Evans, Mark D. J. 1 Gourley, Stephen A. 1 Hairer, Ernst 1 Lambert, J. D. 1 Li, Hongwei 1 Lin, Yanping 1 Ling, Leevan 1 Liu, Rongsong 1 Ma, Yunyun 1 McKee, Sally A. 1 Mustapha, Hussein 1 Mustapha, Kassem 1 Ostermann, Alexander 1 Ou, Chunhua 1 Roth, Helmut 1 Sizikov, Valery 1 Sloan, David M. 1 Song, Huiming 1 Torelli, Lucio 1 van der Houwen, Pieter J. 1 Vermiglio, Rossana 1 Wolkenfelt, Paul H. M. 1 Xiao, Yanyu 1 Xu, Xiuxiu 1 Xu, Yuesheng 1 Yamamoto, Masahiro 1 Yatsenko, Yuri 1 Zhang, Shuhua 1 Zhao, Xiao-Qiang 1 Zou, Xingfu
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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
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#### Fields

 162 Numerical analysis (65-XX) 127 Integral equations (45-XX) 19 Ordinary differential equations (34-XX) 11 Partial differential equations (35-XX) 5 Approximations and expansions (41-XX) 5 Operator theory (47-XX) 5 Biology and other natural sciences (92-XX) 3 Difference and functional equations (39-XX) 2 General and overarching topics; collections (00-XX) 2 Fluid mechanics (76-XX) 1 History and biography (01-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Optics, electromagnetic theory (78-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

157 Publications have been cited 3,017 times in 1,529 Documents Cited by Year
Collocation methods for Volterra integral and related functional differential equations. Zbl 1059.65122
Brunner, Hermann
2004
The numerical solution of Volterra equations. Zbl 0611.65092
Brunner, Hermann; van der Houwen, P. J.
1986
Blowup in diffusion equations: A survey. Zbl 0932.65098
Bandle, Catherine; Brunner, Hermann
1998
The numerical solution of weakly singular Volterra integral equations by collocation on graded meshes. Zbl 0584.65093
Brunner, Herrmann
1985
Numerical simulations of 2D fractional subdiffusion problems. Zbl 1197.65143
Brunner, Hermann; Ling, Leevan; Yamamoto, Masahiro
2010
The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Zbl 0941.65136
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi
1999
On the numerical solution of nonlinear Volterra-Fredholm integral equations by collocation methods. Zbl 0702.65104
Brunner, Hermann
1990
Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels. Zbl 0998.65134
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi
2001
Nonpolynomial spline collocation for Volterra equations with weakly singular kernels. Zbl 0533.65087
Brunner, Hermann
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
2011
$$hp$$-discontinuous Galerkin time-stepping for Volterra integrodifferential equations. Zbl 1116.65127
Brunner, Hermann; Schötzau, Dominik
2006
Stability of numerical methods for Volterra integro-differential equations. Zbl 0282.65088
Brunner, H.; Lambert, J. D.
1974
Spectral methods for pantograph-type differential and integral equations with multiple delays. Zbl 1396.65107
Ali, Ishtiaq; Brunner, Hermann; Tang, Tao
2009
Implicitly linear collocation methods for nonlinear Volterra equations. Zbl 0761.65103
Brunner, Hermann
1992
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.
1987
Polynomial spline collocation methods for Volterra integrodifferential equations with weakly singular kernels. Zbl 0634.65142
Brunner, Hermann
1986
Volterra integral equations. An introduction to theory and applications. Zbl 1376.45002
Brunner, Hermann
2017
A spectral method for pantograph-type delay differential equations and its convergence analysis. Zbl 1212.65308
Ali, Ishtiaq; Brunner, Hermann; Tang, Tao
2009
High-order methods for the numerical solution of Volterra integro- differential equations. Zbl 0634.65143
Brunner, Hermann
1986
Iterated collocation methods and their discretizations for Volterra integral equations. Zbl 0575.65134
Brunner, Hermann
1984
Geometric meshes in collocation methods for Volterra integral equations with proportional delays. Zbl 1014.65143
Brunner, Hermann; Hu, Qiya; Lin, Qun
2001
On the attainable order of collocation methods for pantograph integro-differential equations. Zbl 1023.65146
Muroya, Yoshiaki; Ishiwata, Emiko; Brunner, Hermann
2003
Implicit Runge-Kutta methods of optimal order for Volterra integro- differential equations. Zbl 0543.65092
Brunner, Hermann
1984
Runge-Kutta theory for Volterra integral equations of the second kind. Zbl 0496.65066
Brunner, Hermann; Hairer, Ernst; Nørsett, Syvert P.
1982
A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations. Zbl 0485.65087
Brunner, Hermann
1982
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.
1997
An $$hp$$-version discontinuous Galerkin method for integro-differential equations of parabolic type. Zbl 1230.65143
Mustapha, K.; Brunner, H.; Mustapha, H.; Schötzau, D.
2011
Finite element methods for optimal control problems governed by integral equations and integro-differential equations. Zbl 1076.65057
Brunner, Hermann; Yan, Ningning
2005
The numerical solution of two-dimensional Volterra integral equations by collocation and iterated collocation. Zbl 0665.65095
Brunner, Hermann; Kauthen, J.-P.
1989
The numerical solution of neutral Volterra integro-differential equations with delay arguments. Zbl 0828.65146
Brunner, Hermann
1994
Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind. Zbl 0442.65125
Brunner, Hermann; Nørsett, Syvert P.
1981
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
2014
Iterated collocation methods for Volterra integral equations with delay arguments. Zbl 0803.65139
Brunner, Hermann
1994
Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels. Zbl 1268.65171
Xiang, Shuhuang; Brunner, Hermann
2013
Stability of solutions of delay functional integro-differential equations and their discretizations. Zbl 1049.65150
Brunner, Hermann; Vermiglio, Rossana
2003
Discontinuous Galerkin methods for delay differential equations of pantograph type. Zbl 1219.65076
Brunner, Hermann; Huang, Qiumei; Xie, Hehu
2010
Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays. Zbl 1396.65161
Brunner, Hermann
2009
Integral-algebraic equations: theory of collocation methods. I. Zbl 1280.65147
Liang, Hui; Brunner, Hermann
2013
The spectral problem for a class of highly oscillatory Fredholm integral operators. Zbl 1185.45002
Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
2010
On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations. Zbl 0857.65145
Brunner, Hermann; Yan, Ningning
1996
A family of methods for Abel integral equations of the second kind. Zbl 0724.65130
Brunner, H.; Crisci, M. R.; Russo, E.; Vecchio, A.
1991
Collocation methods for nonlinear Volterra integro-differential equations with infinite delay. Zbl 0681.65105
Brunner, Hermann
1989
The approximate solution of Volterra equations with nonsmooth solutions. Zbl 0563.65077
Brunner, Hermann
1985
Collocation methods for general Volterra functional integral equations with vanishing delays. Zbl 1239.65085
Xie, Hehu; Zhang, Ran; Brunner, Hermann
2011
Numerical analysis of semilinear parabolic problems with blow-up solutions. Zbl 0862.65053
Bandle, C.; Brunner, H.
1994
Discontinuous Galerkin approximations for Volterra integral equations of the first kind. Zbl 1180.65175
Brunner, Hermann; Davies, Penny J.; Duncan, Dugald B.
2009
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.
2006
Optimal superconvergence orders of iterated collocation solutions for Volterra integral equations with vanishing delays. Zbl 1103.65136
Brunner, Hermann; Hu, Qiya
2005
The numerical analysis of functional integral and integro-differential equations of Volterra type. Zbl 1118.65391
Brunner, Hermann
2004
Continuous collocation approximations to solutions of first kind Volterra equations. Zbl 0890.65138
Kauthen, J.-P.; Brunner, H.
1997
On mixed collocation methods for Volterra integral equations with periodic solution. Zbl 0878.65117
Brunner, H.; Makroglou, A.; Miller, R. K.
1997
The numerical treatment of Volterra integro-differential equations with unbounded delay. Zbl 0687.65131
Brunner, Hermann
1989
Collocation methods for second-order Volterra integro-differential equations. Zbl 0651.65098
Aguilar, M.; Brunner, Hermann
1988
Optimal superconvergence results for delay integro-differential equations of Pantograph type. Zbl 1144.65083
Brunner, Hermann; Hu, Qiya
2007
On the discretization of differential and Volterra integral equations with variable delay. Zbl 0873.65126
Brunner, Hermann
1997
The approximate solution of initial-value problems for general Volterra integro-differential equations. Zbl 0631.65141
Brunner, Hermann
1988
On the numerical solution of nonlinear Volterra integro-differential equations. Zbl 0265.65056
Brunner, H.
1973
Collocation methods for third-kind vies. Zbl 1433.65345
Allaei, Sonia Seyed; Yang, Zhan-Wen; Brunner, Hermann
2017
Recent advances in the numerical analysis of Volterra functional differential equations with variable delays. Zbl 1170.65103
Brunner, Hermann
2009
Polynomial spline collocation methods for the nonlinear Basset equation. Zbl 0687.65130
Brunner, H.; Tang, T.
1989
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.
1980
Discretization of Volterra integral equations of the first kind. II. Zbl 0366.65058
Brunner, Hermann
1978
The maximum principle for time-fractional diffusion equations and its application. Zbl 1333.65093
Brunner, Hermann; Han, Houde; Yin, Dongsheng
2015
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
2015
Blow-up behavior of Hammerstein-type Volterra integral equations. Zbl 1261.45003
Brunner, H.; Yang, Z. W.
2012
A super-attainable order in collocation methods for differential equations with proportional delay. Zbl 1137.65047
Ishiwata, Emiko; Muroya, Yoshiaki; Brunner, Hermann
2008
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
1998
On implicitly linear and iterated collocation methods for Hammerstein integral equations. Zbl 0749.65090
Brunner, Hermann
1991
Discretization of Volterra integral equations of the first kind. Zbl 0372.65052
Brunner, Hermann
1977
Analysis of collocation solutions for a class of functional equations with vanishing delays. Zbl 1259.65205
Brunner, Hermann; Xie, Hehu; Zhang, Ran
2011
Stability of collocation methods for delay differential equations with vanishing delays. Zbl 1205.65223
Brunner, Hermann; Liang, Hui
2010
1896–1996: One hundred years of Volterra integral equations of the first kind. Zbl 0879.45001
Brunner, Hermann
1997
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.
1984
Superconvergence of collocation methods for Volterra integral equations of the first kind. Zbl 0391.65055
Brunner, Hermann
1979
Piecewise polynomial collocation for Volterra-type integral equations of the second kind. Zbl 0382.65065
Brunner, H.; Evans, M. D.
1977
The $$hp$$ discontinuous Galerkin method for delay differential equations with nonlinear vanishing delay. Zbl 1276.65039
Huang, Qiumei; Xie, Hehu; Brunner, Hermann
2013
Numerical blow-up of semilinear parabolic PDEs on unbounded domains in $$\mathbb R^{2}$$. Zbl 1244.65128
Zhang, Jiwei; Han, Houde; Brunner, Hermann
2011
The computation of the spectra of highly oscillatory Fredholm integral operators. Zbl 1238.65123
Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
2011
Computational solution of blow-up problems for semilinear parabolic PDEs on unbounded domains. Zbl 1208.65124
Brunner, Hermann; Wu, Xiaonan; Zhang, Jiwei
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
2005
Primary discontinuities in solutions for delay integro-differential equations. Zbl 0959.45002
Brunner, Hermann; Zhang, Wenkui
1999
Superconvergence of discontinuous Galerkin solutions for delay differential equations of pantograph type. Zbl 1232.65102
Huang, Qiumei; Xie, Hehu; Brunner, Hermann
2011
High-order collocation methods for singular Volterra functional equations of neutral type. Zbl 1119.65121
Brunner, Hermann
2007
A posteriori error estimates of discontinuous Galerkin methods for non-standard Volterra integro-differential equations. Zbl 1094.65135
Ma, Jingtang; Brunner, Hermann
2006
The iterative correction method for Volterra integral equations. Zbl 0854.65121
Brunner, Hermann; Lin, Qun; Yan, Ningning
1996
Implicit Runge-Kutta-Nyström methods for general second-order Volterra integro differential equations. Zbl 0632.65137
Brunner, H.
1987
The solution of Volterra integral equations of the first kind by piecewise polynomials. Zbl 0271.65066
Brunner, H.
1973
Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type. Zbl 1351.65047
Huang, Qiumei; Xu, Xiuxiu; Brunner, Hermann
2016
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.
2010
Runge-Kutta time discretizations of parabolic Volterra integro- differential equations. Zbl 0832.65141
Brunner, H.; Kauthen, J.-P.; Ostermann, A.
1995
Collocation and continuous implicit Runge-Kutta methods for a class of delay Volterra integral equations. Zbl 0818.65134
Brunner, Hermann
1994
Algorithm 689: Discretized collocation and iterated collocation for nonlinear Volterra integral equations of the second kind. Zbl 0900.65382
Blom, J. G.; Brunner, H.
1991
The application of the variation of constants formulas in the numerical analysis of integral and integro-differential equations. Zbl 0483.65034
Brunner, Hermann
1981
On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations. Zbl 1356.65261
Liang, Hui; Brunner, Hermann
2016
On Volterra integral operators with highly oscillatory kernels. Zbl 1278.45016
Brunner, Hermann
2014
The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays. Zbl 1133.65112
Brunner, Hermann
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
2006
The dicretization of neutral functional integro-differential equations by collocation methods. Zbl 0951.65149
Brunner, H.
1999
On discrete superconvergence properties of spline collocation methods for nonlinear Volterra integral equations. Zbl 0758.65083
Brunner, Hermann
1992
The convergence of collocation solutions in continuous piecewise polynomial spaces for weakly singular Volterra integral equations. Zbl 1420.65139
Liang, Hui; Brunner, Hermann
2019
Collocation methods for integro-differential algebraic equations with index 1. Zbl 07199495
Liang, Hui; Brunner, Hermann
2020
The convergence of collocation solutions in continuous piecewise polynomial spaces for weakly singular Volterra integral equations. Zbl 1420.65139
Liang, Hui; Brunner, Hermann
2019
Analysis of collocation methods for nonlinear Volterra integral equations of the third kind. Zbl 1434.65320
Song, Huiming; Yang, Zhanwen; Brunner, Hermann
2019
Numerical analysis and computational solution of integro-differential equations. Zbl 1405.65165
Brunner, Hermann
2018
Volterra integral equations. An introduction to theory and applications. Zbl 1376.45002
Brunner, Hermann
2017
Collocation methods for third-kind vies. Zbl 1433.65345
Allaei, Sonia Seyed; Yang, Zhan-Wen; Brunner, Hermann
2017
Pauses of larval development and their consequences for stage-structured populations. Zbl 1367.92095
Brunner, Hermann; Gourley, Stephen A.; Liu, Rongsong; Xiao, Yanyu
2017
Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type. Zbl 1351.65047
Huang, Qiumei; Xu, Xiuxiu; Brunner, Hermann
2016
On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations. Zbl 1356.65261
Liang, Hui; Brunner, Hermann
2016
Integral-algebraic equations: Theory of collocation methods. II. Zbl 1347.65196
Liang, Hui; Brunner, Hermann
2016
Analysis of collocation methods for generalized auto-convolution Volterra integral equations. Zbl 1416.65560
Zhang, Ran; Liang, Hui; Brunner, Hermann
2016
Numerical blow-up of nonlinear parabolic integro-differential equations on unbounded domain. Zbl 1352.65651
Brunner, Hermann; Tang, Tao; Zhang, Jiwei
2016
The maximum principle for time-fractional diffusion equations and its application. Zbl 1333.65093
Brunner, Hermann; Han, Houde; Yin, Dongsheng
2015
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
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
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
2014
On Volterra integral operators with highly oscillatory kernels. Zbl 1278.45016
Brunner, Hermann
2014
Efficient methods for Volterra integral equations with highly oscillatory Bessel kernels. Zbl 1268.65171
Xiang, Shuhuang; Brunner, Hermann
2013
Integral-algebraic equations: theory of collocation methods. I. Zbl 1280.65147
Liang, Hui; Brunner, Hermann
2013
The $$hp$$ discontinuous Galerkin method for delay differential equations with nonlinear vanishing delay. Zbl 1276.65039
Huang, Qiumei; Xie, Hehu; Brunner, Hermann
2013
Blow-up behavior of collocation solutions to Hammerstein-type Volterra integral equations. Zbl 1277.65117
Yang, Z. W.; Brunner, H.
2013
Blow-up behavior of Hammerstein-type delay Volterra integral equations. Zbl 1273.45001
Yang, Zhanwen; Brunner, Hermann
2013
Erratum to “Clenshaw-Curtis-Filon-type methods for highly oscillatory Bessel transforms and applications”. Zbl 06220963
Xiang, Shuhuang; Cho, Yeol Je; Wang, Haiyong; Brunner, Hermann
2013
Blow-up behavior of Hammerstein-type Volterra integral equations. Zbl 1261.45003
Brunner, H.; Yang, Z. W.
2012
Collocation methods for differential equations with piecewise linear delays. Zbl 1264.65124
Liang, Hui; Brunner, Hermann
2012
Discrete superconvergence of collocation solutions for first-kind Volterra integral equations. Zbl 1259.65216
Liang, Hui; Brunner, Hermann
2012
Asymptotic stability of solutions to Volterra-renewal integral equations with space maps. Zbl 1254.45012
Annunziato, M.; Brunner, H.; Messina, E.
2012
Asymptotic periodicity of nonlinear discrete Volterra equations and applications. Zbl 1254.39005
Cardone, Angelamaria; Del Prete, Ida; Brunner, Hermann
2012
Global convergence and local superconvergence of first-kind Volterra integral equation approximations. Zbl 1252.65208
Brunner, Hermann; Davies, Penny J.; Duncan, Dugald B.
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
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.
2011
Collocation methods for general Volterra functional integral equations with vanishing delays. Zbl 1239.65085
Xie, Hehu; Zhang, Ran; Brunner, Hermann
2011
Analysis of collocation solutions for a class of functional equations with vanishing delays. Zbl 1259.65205
Brunner, Hermann; Xie, Hehu; Zhang, Ran
2011
Numerical blow-up of semilinear parabolic PDEs on unbounded domains in $$\mathbb R^{2}$$. Zbl 1244.65128
Zhang, Jiwei; Han, Houde; Brunner, Hermann
2011
The computation of the spectra of highly oscillatory Fredholm integral operators. Zbl 1238.65123
Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
2011
Superconvergence of discontinuous Galerkin solutions for delay differential equations of pantograph type. Zbl 1232.65102
Huang, Qiumei; Xie, Hehu; Brunner, Hermann
2011
Numerical simulations of 2D fractional subdiffusion problems. Zbl 1197.65143
Brunner, Hermann; Ling, Leevan; Yamamoto, Masahiro
2010
Discontinuous Galerkin methods for delay differential equations of pantograph type. Zbl 1219.65076
Brunner, Hermann; Huang, Qiumei; Xie, Hehu
2010
The spectral problem for a class of highly oscillatory Fredholm integral operators. Zbl 1185.45002
Brunner, Hermann; Iserles, Arieh; Nørsett, Syvert P.
2010
Stability of collocation methods for delay differential equations with vanishing delays. Zbl 1205.65223
Brunner, Hermann; Liang, Hui
2010
Computational solution of blow-up problems for semilinear parabolic PDEs on unbounded domains. Zbl 1208.65124
Brunner, Hermann; Wu, Xiaonan; Zhang, Jiwei
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.
2010
Time transformations for state-dependent delay differential equations. Zbl 1194.34135
Brunner, Hermann; Maset, Stefano
2010
Spectral methods for pantograph-type differential and integral equations with multiple delays. Zbl 1396.65107
Ali, Ishtiaq; Brunner, Hermann; Tang, Tao
2009
A spectral method for pantograph-type delay differential equations and its convergence analysis. Zbl 1212.65308
Ali, Ishtiaq; Brunner, Hermann; Tang, Tao
2009
Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays. Zbl 1396.65161
Brunner, Hermann
2009
Discontinuous Galerkin approximations for Volterra integral equations of the first kind. Zbl 1180.65175
Brunner, Hermann; Davies, Penny J.; Duncan, Dugald B.
2009
Recent advances in the numerical analysis of Volterra functional differential equations with variable delays. Zbl 1170.65103
Brunner, Hermann
2009
Time transformations for delay differential equations. Zbl 1187.34093
Brunner, Hermann; Maset, Stefano
2009
A super-attainable order in collocation methods for differential equations with proportional delay. Zbl 1137.65047
Ishiwata, Emiko; Muroya, Yoshiaki; Brunner, Hermann
2008
Collocation methods for pantograph-type Volterra functional equations with multiple delays. Zbl 1153.65123
Brunner, H.
2008
Optimal superconvergence results for delay integro-differential equations of Pantograph type. Zbl 1144.65083
Brunner, Hermann; Hu, Qiya
2007
High-order collocation methods for singular Volterra functional equations of neutral type. Zbl 1119.65121
Brunner, Hermann
2007
$$hp$$-discontinuous Galerkin time-stepping for Volterra integrodifferential equations. Zbl 1116.65127
Brunner, Hermann; Schötzau, Dominik
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.
2006
A posteriori error estimates of discontinuous Galerkin methods for non-standard Volterra integro-differential equations. Zbl 1094.65135
Ma, Jingtang; Brunner, Hermann
2006
The numerical solution of weakly singular Volterra functional integro-differential equations with variable delays. Zbl 1133.65112
Brunner, Hermann
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
2006
On the regularity of solutions to Volterra functional integro-differential equations with weakly singular kernels. Zbl 1147.45007
Brunner, Hermann; Ma, Jingtang
2006
Abstract cascading multigrid preconditioners in Besov spaces. Zbl 1133.65074
Ma, Jingtang; Brunner, Hermann
2006
Finite element methods for optimal control problems governed by integral equations and integro-differential equations. Zbl 1076.65057
Brunner, Hermann; Yan, Ningning
2005
Optimal superconvergence orders of iterated collocation solutions for Volterra integral equations with vanishing delays. Zbl 1103.65136
Brunner, Hermann; Hu, Qiya
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
2005
Collocation methods for Volterra integral and related functional differential equations. Zbl 1059.65122
Brunner, Hermann
2004
The numerical analysis of functional integral and integro-differential equations of Volterra type. Zbl 1118.65391
Brunner, Hermann
2004
On the divergence of collocation solutions in smooth piecewise polynomial spaces for Volterra integral equations. Zbl 1079.65131
Brunner, Hermann
2004
The discretizaton of Volterra functional integral equations with proportional delays. Zbl 1067.65149
Brunner, Hermann
2004
Discretization of Volterra integral equations with weakly singular kernels. Zbl 1060.65683
Brunner, Hermann
2004
On the attainable order of collocation methods for pantograph integro-differential equations. Zbl 1023.65146
Muroya, Yoshiaki; Ishiwata, Emiko; Brunner, Hermann
2003
Stability of solutions of delay functional integro-differential equations and their discretizations. Zbl 1049.65150
Brunner, Hermann; Vermiglio, Rossana
2003
Time-stepping methods for Volterra-Fredholm integral equations. Zbl 1095.65117
Brunner, Hermann; Messina, Eleonora
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.
2002
Piecewise polynomial collocation methods for linear Volterra integro-differential equations with weakly singular kernels. Zbl 0998.65134
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi
2001
Geometric meshes in collocation methods for Volterra integral equations with proportional delays. Zbl 1014.65143
Brunner, Hermann; Hu, Qiya; Lin, Qun
2001
The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations. Zbl 0941.65136
Brunner, Hermann; Pedas, Arvet; Vainikko, Gennadi
1999
Primary discontinuities in solutions for delay integro-differential equations. Zbl 0959.45002
Brunner, Hermann; Zhang, Wenkui
1999
The dicretization of neutral functional integro-differential equations by collocation methods. Zbl 0951.65149
Brunner, H.
1999
The use of splines in the numerical solution of differential and Volterra integral equations. Zbl 0969.65065
Brunner, Hermann
1999
The numerical solution of weakly singular first-kind Volterra integral equations with delay arguments. Zbl 0967.65116
Brunner, Hermann
1999
On systems of Volterra difference equations associated with collocation methods for weakly singular Volterra integral equations. Zbl 0938.65154
Brunner, Hermann
1999
Blowup in diffusion equations: A survey. Zbl 0932.65098
Bandle, Catherine; Brunner, Hermann
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
1998
Collocation approximations for second-order differential equations and Volterra integro-differential equations with variable delays. Zbl 0924.65140
Zhang, Wenkui; Brunner, Hermann
1998
On a suboptimal filtration method for solving convolution-type integral equations of the first kind. Zbl 0915.65138
Brunner, Hermann; Sizikov, Valery
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.
1997
Continuous collocation approximations to solutions of first kind Volterra equations. Zbl 0890.65138
Kauthen, J.-P.; Brunner, H.
1997
On mixed collocation methods for Volterra integral equations with periodic solution. Zbl 0878.65117
Brunner, H.; Makroglou, A.; Miller, R. K.
1997
On the discretization of differential and Volterra integral equations with variable delay. Zbl 0873.65126
Brunner, Hermann
1997
1896–1996: One hundred years of Volterra integral equations of the first kind. Zbl 0879.45001
Brunner, Hermann
1997
On global superconvergence of iterated collocation solutions to linear second-kind Volterra integral equations. Zbl 0857.65145
Brunner, Hermann; Yan, Ningning
1996
The iterative correction method for Volterra integral equations. Zbl 0854.65121
Brunner, Hermann; Lin, Qun; Yan, Ningning
1996
Open problems in the discretization of Volterra integral equations. Zbl 0882.65140
Brunner, Hermann
1996
Spline collocation methods for nonlinear Volterra integral equations with unknown delay. Zbl 0855.65143
Brunner, Hermann; Yatsenko, Yuri
1996
Runge-Kutta time discretizations of parabolic Volterra integro- differential equations. Zbl 0832.65141
Brunner, H.; Kauthen, J.-P.; Ostermann, A.
1995
The numerical solution of neutral Volterra integro-differential equations with delay arguments. Zbl 0828.65146
Brunner, Hermann
1994
Iterated collocation methods for Volterra integral equations with delay arguments. Zbl 0803.65139
Brunner, Hermann
1994
Numerical analysis of semilinear parabolic problems with blow-up solutions. Zbl 0862.65053
Bandle, C.; Brunner, H.
1994
Collocation and continuous implicit Runge-Kutta methods for a class of delay Volterra integral equations. Zbl 0818.65134
Brunner, Hermann
1994
The numerical treatment of ordinary and partial Volterra integro-differential equations. Zbl 0847.65087
Brunner, Hermann
1993
Continuous Volterra-Runge-Kutta methods for integral equations with pure delay. Zbl 0782.65150
1993
...and 57 more Documents
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#### Cited by 1,707 Authors

 75 Brunner, Hermann 26 Maleknejad, Khosrow 26 Vecchio, Antonia 26 Xiang, Shuhuang 24 Pedas, Arvet 24 Zhang, Chengjian 20 Huang, Chengming 17 Liang, Hui 17 Yi, Lijun 16 Baker, Christopher T. H. 16 Chen, Yanping 16 Jackiewicz, Zdzislaw 16 Vainikko, Gennadi M. 16 Wang, Wansheng 15 Crisci, Maria Rosaria 15 Russo, Elvira 15 Zhang, Jiwei 14 Conte, Dajana 14 Tamme, Enn 13 Dehghan Takht Fooladi, Mehdi 13 Diogo, Teresa 13 Ma, Jingtang 13 Messina, Eleonora 13 Tang, Tao 13 Yang, Zhanwen 12 Nelakanti, Gnaneshwar 12 Sezer, Mehmet 12 Sun, Zhizhong 11 Cardone, Angelamaria 11 Ford, Neville J. 11 Hadizadeh, Mahmoud 11 Kang, Hongchao 11 Li, Dongfang 11 Lima, Pedro Miguel 11 Ma, Junjie 11 Paternoster, Beatrice 11 Rossi, Julio Daniel 11 Zhao, Jingjun 10 Abdi, Ali 10 Gu, Zhendong 10 Mustapha, Kassem 9 Bulatov, Mikhail Valer’yanovich 9 Garey, L. E. 9 Groisman, Pablo 9 Hojjati, Gholamreza 9 Kolmanovskii, Vladimir Borisovich 9 Liao, HongLin 9 Shahmorad, Sedaghat 9 Song, Yihong 9 Stynes, Martin 9 van der Houwen, Pieter J. 9 Xu, Zhenhua 8 Băleanu, Dumitru I. 8 Cai, Haotao 8 Chen, Ruyun 8 Ding, Juntang 8 He, Guo 8 Lin, Yanping 8 Makroglou, Athena 8 McKee, Sean 8 Pishbin, Saeed 8 Wang, Zhongqing 8 Xu, Yang 8 Yüzbaşı, Şuayip 8 Zhang, Zhimin 7 Bellen, Alfredo 7 Gladwin, Charles J. 7 Kauthen, Jean-Paul 7 Laeli Dastjerdi, H. 7 Li, Shoufu 7 Ling, Leevan 7 Lu, Zuliang 7 Mokhtary, Payam 7 Payne, Lawrence Edward 7 Vermiglio, Rossana 7 Wen, Liping 7 Zhang, Shuhua 6 Berenguer, María Isabel 6 D’Ambrosio, Raffaele 6 Han, Guoqiang 6 Jiang, Yingjun 6 Li, Fengjie 6 Liu, Bingchen 6 Mandal, Moumita 6 Mirzaee, Farshid 6 Ordokhani, Yadollah 6 Philippin, Gérard A. 6 Razzaghi, Mohsen 6 Sheng, Qin 6 Wang, Lina 6 Wazwaz, Abdul-Majid Abdul-Rahman 6 Wei, Yunxia 6 Xu, Da 6 Xu, Yuesheng 5 Alnasr, Modi H. 5 Bazm, Sohrab 5 Capobianco, Giovanni 5 Fang, Chunhua 5 Fazeli, Somayyeh 5 Gao, Jianfang ...and 1,607 more Authors
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#### Cited in 214 Serials

 197 Journal of Computational and Applied Mathematics 164 Applied Mathematics and Computation 119 Applied Numerical Mathematics 48 Journal of Scientific Computing 48 Journal of Integral Equations and Applications 42 Numerical Algorithms 39 Computers & Mathematics with Applications 35 International Journal of Computer Mathematics 34 Journal of Mathematical Analysis and Applications 31 BIT 31 Numerische Mathematik 29 Journal of Computational Physics 27 Computational and Applied Mathematics 26 Mathematics of Computation 24 Abstract and Applied Analysis 22 Advances in Computational Mathematics 21 SIAM Journal on Numerical Analysis 20 Computing 19 Applied Mathematical Modelling 16 Frontiers of Mathematics in China 15 Numerical Functional Analysis and Optimization 14 Advances in Difference Equations 13 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 13 SIAM Journal on Scientific Computing 12 Calcolo 12 Engineering Analysis with Boundary Elements 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 10 Mathematical and Computer Modelling 10 Mathematical Problems in Engineering 10 Discrete and Continuous Dynamical Systems. Series B 9 Mathematics and Computers in Simulation 9 Applied Mathematics Letters 9 Journal of Applied Mathematics 9 Journal of Applied Mathematics and Computing 8 Applicable Analysis 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 Chaos, Solitons and Fractals 6 Applications of Mathematics 6 Mediterranean Journal of Mathematics 6 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 5 Discrete and Continuous Dynamical Systems 5 Fractional Calculus & Applied Analysis 5 Lobachevskii Journal of Mathematics 5 Nonlinear Analysis. Real World Applications 5 BIT. Nordisk Tidskrift for Informationsbehandling 4 Turkish Journal of Mathematics 4 Journal of Inequalities and Applications 4 Computational Methods in Applied Mathematics 4 Asian-European Journal of Mathematics 4 Science China. Mathematics 4 Symmetry 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 Discrete Dynamics in Nature and Society 3 Differential Equations 3 International Journal of Computational Methods 3 Discrete and Continuous Dynamical Systems. Series S 3 Advances in Mathematical Physics 3 Mathematical Sciences 3 Nonlinear Analysis. Theory, Methods & Applications 2 Computers and Fluids 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 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 Journal of Fixed Point Theory and Applications 2 Inverse Problems and Imaging 2 Advances in Differential Equations and Control Processes 2 Vestnik Yuzhno-Ural’skogo Gosudarstvennogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie 2 Mathematical Control and Related Fields ...and 114 more Serials
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#### Cited in 45 Fields

 1,265 Numerical analysis (65-XX) 866 Integral equations (45-XX) 302 Partial differential equations (35-XX) 219 Ordinary differential equations (34-XX) 62 Real functions (26-XX) 54 Approximations and expansions (41-XX) 46 Operator theory (47-XX) 35 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) 24 Difference and functional equations (39-XX) 23 Mechanics of deformable solids (74-XX) 18 Fluid mechanics (76-XX) 16 Harmonic analysis on Euclidean spaces (42-XX) 16 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 Integral transforms, operational calculus (44-XX) 13 Statistical mechanics, structure of matter (82-XX) 12 Optics, electromagnetic theory (78-XX) 10 Dynamical systems and ergodic theory (37-XX) 10 Classical thermodynamics, heat transfer (80-XX) 10 Systems theory; control (93-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) 6 Computer science (68-XX) 5 History and biography (01-XX) 3 Combinatorics (05-XX) 3 Functions of a complex variable (30-XX) 3 Potential theory (31-XX) 3 Mechanics of particles and systems (70-XX) 2 Number theory (11-XX) 2 Field theory and polynomials (12-XX) 2 Sequences, series, summability (40-XX) 2 Quantum theory (81-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Mathematics education (97-XX)

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