Edit Profile (opens in new tab) Herbst, Barend M. Compute Distance To: Compute Author ID: herbst.barend-m Published as: Herbst, Barend M. Documents Indexed: 44 Publications since 1979 1 Further Contribution Co-Authors: 4 Co-Authors with 1 Joint Publication 53 Co-Co-Authors all top 5 Co-Authors 4 single-authored 18 Ablowitz, Mark Jay 7 Schober, Constance M. 7 Weideman, J. André C. 6 Mitchell, Andrew Ronald 4 Cloot, Alain H. J. J. 3 Schoombie, Schalk W. 1 Adams, Paul J. 1 Babuška, Ivo 1 Bischoff, Dieter Ernst 1 Botha, Joseph F. 1 Brand, G. F. 1 Coffignal, G. 1 de Arantes Oliveira, E. R. 1 De Villiers, Johan Marthinus 1 Demkowicz, Leszek F. 1 Devloo, Philippe Remy Bernard 1 du Preez, Johan A. 1 Eklund, Holly L. 1 Fairweather, Graeme 1 Gago, J. 1 Goosen, K. M. 1 Griffiths, David F. 1 Hereman, Willy A. 1 Hickman, Mark S. 1 Keiser, James M. 1 Kelly, Donald W. 1 Ladevèze, Pierre 1 Löhner, Rainald 1 Magaia, Lourenço 1 Molchan, Maxim A. 1 Morris, John Ll. 1 Muller, Neil 1 Nel, Emli-Mari 1 Oden, John Tinsley 1 Olivier, C. P. 1 Pelle, Jean-Pierre 1 Plank, Lothar 1 Rank, Ernst 1 Rheinboldt, C. 1 Robinson, Mark P. 1 Ryan, Eoghan 1 Sloan, David M. 1 Stein, Erwin 1 Strouboulis, Theofanis 1 Varadi, Ferenc 1 Zienkiewicz, Olgierd Cecil all top 5 Serials 8 Journal of Computational Physics 3 International Journal for Numerical Methods in Engineering 3 Mathematics and Computers in Simulation 2 IMA Journal of Numerical Analysis 2 Journal of Computational and Applied Mathematics 1 Computer Physics Communications 1 Inverse Problems 1 Nonlinearity 1 Quaestiones Mathematicae 1 SIAM Journal on Numerical Analysis 1 SIAM Journal on Scientific and Statistical Computing 1 Acta Applicandae Mathematicae 1 Physica D 1 Applied Numerical Mathematics 1 Communications in Applied Numerical Methods 1 Journal of Physics A: Mathematical and General 1 Pattern Recognition 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 Journal of Physics A: Mathematical and Theoretical all top 5 Fields 32 Partial differential equations (35-XX) 32 Numerical analysis (65-XX) 11 Dynamical systems and ergodic theory (37-XX) 7 Quantum theory (81-XX) 6 Ordinary differential equations (34-XX) 6 Computer science (68-XX) 5 Fluid mechanics (76-XX) 2 Mechanics of particles and systems (70-XX) 1 General and overarching topics; collections (00-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 36 Publications have been cited 16 times in 16 Documents Cited by ▼ Year ▼ On the extension of the Painlevé property to difference equations. Zbl 0956.39003Ablowitz, M. J.; Halburd, R.; Herbst, B. 108 2000 Split-step methods for the solution of the nonlinear Schrödinger equation. Zbl 0597.76012Weideman, J. A. C.; Herbst, B. M. 107 1986 On the numerical solution of the sine-Gordon equation. I: Integrable discretizations and homoclinic manifolds. Zbl 0866.65064Ablowitz, M. J.; Herbst, B. M.; Schober, Constance 69 1996 On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation. Zbl 0707.35141Ablowitz, Mark J.; Herbst, B. M. 56 1990 Accuracy estimates and adaptive refinements in finite element computations. Lectures presented at the international conference held in Lisbon, June 1984. Zbl 0663.65001 44 1986 On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes. Zbl 0874.65076Ablowitz, M. J.; Herbst, B. M.; Schober, C. M. 28 1997 Numerical experience with the nonlinear Schrödinger equation. Zbl 0589.65084Herbst, B. M.; Morris, J. Ll.; Mitchell, A. R. 26 1985 A moving Petrov-Galerkin method for transport equations. Zbl 0485.65093Herbst, B. M.; Schoombie, S. W.; Mitchell, A. R. 25 1982 Numerical homoclinic instabilities and the complex modified Korteweg-de Vries equation. Zbl 0900.65350Herbst, B. M.; Ablowitz, Mark J.; Ryan, E. 25 1991 Direct methods and symbolic software for conservation laws of nonlinear equations. Zbl 1210.35164Hereman, Willy; Adams, Paul J.; Eklund, Holly L.; Hickman, Mark S.; Herbst, Barend M. 16 2009 Numerical simulation of quasi-periodic solutions of the sine-Gordon equation. Zbl 1194.65121Ablowitz, Mark J.; Herbst, B. M.; Schober, Constance M. 15 1995 Singular value decomposition, eigenfaces, and 3D reconstructions. Zbl 1061.65033Muller, Neil; Magaia, Lourenço; Herbst, B. M. 13 2004 Numerical homoclinic instabilities in the sine-Gordon equation. Zbl 0785.65086Herbst, B. M.; Ablowitz, M. J. 11 1992 Symplectic methods for the nonlinear Schrödinger equation. Zbl 0812.65118Herbst, B. M.; Varadi, F.; Ablowitz, M. J. 10 1994 Generalized Petrov-Galerkin methods for the numerical solution of Burgers’ equation. Zbl 0546.65078Herbst, B. M.; Schoombie, S. W.; Griffiths, D. F.; Mitchell, A. R. 9 1984 A numerical study of the nonlinear Schrödinger equation involving quintic terms. Zbl 0685.65110Cloot, A.; Herbst, B. M.; Weideman, J. A. C. 8 1990 Discretizations, integrable systems and computation. Zbl 0991.65137Ablowitz, M. J.; Herbst, B. M.; Schober, C. M. 8 2001 Dubuc–Deslauriers subdivision for finite sequences and interpolation wavelets on an interval. Zbl 1047.65121de Villiers, J. M.; Goosen, K. M.; Herbst, B. M. 8 2003 On the stability of the nonlinear Schrödinger equation. Zbl 0589.65083Herbst, B. M.; Mitchell, A. R.; Weideman, J. A. C. 7 1985 Equidistributing principles in moving finite element methods. Zbl 0532.65074Herbst, B. M.; Schoombie, S. W.; Mitchell, A. R. 6 1983 On the numerical solution of the cubic Schrödinger equation in one space variable. Zbl 0766.65112Robinson, M. P.; Fairweather, G.; Herbst, B. M. 6 1993 Numerical chaos, symplectic integrators, and exponentially small splitting distances. Zbl 0772.65084Herbst, B. M.; Ablowitz, Mark J. 6 1993 Recurrence in semidiscrete approximations of the nonlinear Schrödinger equation. Zbl 0646.65088Weideman, J. A. C.; Herbst, B. M. 5 1987 On numerical chaos in the nonlinear Schrödinger equation. Zbl 0711.35131Herbst, B. M.; Ablowitz, Mark J. 4 1989 Dynamics of semi-discretizations of the defocusing nonlinear Schrödinger equation. Zbl 0737.65088Ablowitz, M. J.; Herbst, B. M.; Weideman, J. A. C. 4 1991 The nonlinear Schrödinger equation: Asymmetric perturbations, traveling waves and chaotic structures. Zbl 0869.68125Ablowitz, M. J.; Herbst, B. M.; Schober, C. M. 4 1997 Analytical instability of the Klein-Gordon equation. Zbl 0634.76047Cloot, A. H. J.; Herbst, B. M. 3 1988 On homoclinic boundaries in the nonlinear Schrödinger equation. Zbl 0736.35105Ablowitz, Mark J.; Herbst, B. M. 2 1990 Nonlinear evolution equations, solitons, chaos and cellular automata. Zbl 0728.35102Ablowitz, M. J.; Herbst, B. M.; Keiser, J. M. 2 1990 On the numerics of integrable discretizations. Zbl 0856.65107Ablowitz, M. J.; Herbst, B. M.; Schober, C. 2 1996 Integrability, computation and applications. Zbl 0832.58019Ablowitz, M. J.; Chakravarty, S.; Herbst, B. M. 2 1995 A model for the propagation of rounding error in a Klein-Gordon equation. Zbl 0683.65105Cloot, A.; Herbst, B. M. 1 1989 Numerical evidence of exponentially small splitting distances in symplectic discretizations of planar Hamiltonian systems. Zbl 0941.37504Herbst, B. M. 1 1992 A note on an integrable discretization of the nonlinear Schrödinger equation. Zbl 0940.35184Black, W.; Weideman, J. A. C.; Herbst, B. M. 1 1999 Finite difference methods for an AKNS eigenproblem. Zbl 0870.65069Weideman, J. A. C.; Herbst, B. M. 1 1997 A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials. Zbl 1258.37068Olivier, C. P.; Herbst, B. M.; Molchan, M. A. 1 2012 A numerical study of the large-period limit of a Zakharov-Shabat eigenvalue problem with periodic potentials. Zbl 1258.37068Olivier, C. P.; Herbst, B. M.; Molchan, M. A. 1 2012 Direct methods and symbolic software for conservation laws of nonlinear equations. Zbl 1210.35164Hereman, Willy; Adams, Paul J.; Eklund, Holly L.; Hickman, Mark S.; Herbst, Barend M. 16 2009 Singular value decomposition, eigenfaces, and 3D reconstructions. Zbl 1061.65033Muller, Neil; Magaia, Lourenço; Herbst, B. M. 13 2004 Dubuc–Deslauriers subdivision for finite sequences and interpolation wavelets on an interval. Zbl 1047.65121de Villiers, J. M.; Goosen, K. M.; Herbst, B. M. 8 2003 Discretizations, integrable systems and computation. Zbl 0991.65137Ablowitz, M. J.; Herbst, B. M.; Schober, C. M. 8 2001 On the extension of the Painlevé property to difference equations. Zbl 0956.39003Ablowitz, M. J.; Halburd, R.; Herbst, B. 108 2000 A note on an integrable discretization of the nonlinear Schrödinger equation. Zbl 0940.35184Black, W.; Weideman, J. A. C.; Herbst, B. M. 1 1999 On the numerical solution of the sine-Gordon equation. II: Performance of numerical schemes. Zbl 0874.65076Ablowitz, M. J.; Herbst, B. M.; Schober, C. M. 28 1997 The nonlinear Schrödinger equation: Asymmetric perturbations, traveling waves and chaotic structures. Zbl 0869.68125Ablowitz, M. J.; Herbst, B. M.; Schober, C. M. 4 1997 Finite difference methods for an AKNS eigenproblem. Zbl 0870.65069Weideman, J. A. C.; Herbst, B. M. 1 1997 On the numerical solution of the sine-Gordon equation. I: Integrable discretizations and homoclinic manifolds. Zbl 0866.65064Ablowitz, M. J.; Herbst, B. M.; Schober, Constance 69 1996 On the numerics of integrable discretizations. Zbl 0856.65107Ablowitz, M. J.; Herbst, B. M.; Schober, C. 2 1996 Numerical simulation of quasi-periodic solutions of the sine-Gordon equation. Zbl 1194.65121Ablowitz, Mark J.; Herbst, B. M.; Schober, Constance M. 15 1995 Integrability, computation and applications. Zbl 0832.58019Ablowitz, M. J.; Chakravarty, S.; Herbst, B. M. 2 1995 Symplectic methods for the nonlinear Schrödinger equation. Zbl 0812.65118Herbst, B. M.; Varadi, F.; Ablowitz, M. J. 10 1994 On the numerical solution of the cubic Schrödinger equation in one space variable. Zbl 0766.65112Robinson, M. P.; Fairweather, G.; Herbst, B. M. 6 1993 Numerical chaos, symplectic integrators, and exponentially small splitting distances. Zbl 0772.65084Herbst, B. M.; Ablowitz, Mark J. 6 1993 Numerical homoclinic instabilities in the sine-Gordon equation. Zbl 0785.65086Herbst, B. M.; Ablowitz, M. J. 11 1992 Numerical evidence of exponentially small splitting distances in symplectic discretizations of planar Hamiltonian systems. Zbl 0941.37504Herbst, B. M. 1 1992 Numerical homoclinic instabilities and the complex modified Korteweg-de Vries equation. Zbl 0900.65350Herbst, B. M.; Ablowitz, Mark J.; Ryan, E. 25 1991 Dynamics of semi-discretizations of the defocusing nonlinear Schrödinger equation. Zbl 0737.65088Ablowitz, M. J.; Herbst, B. M.; Weideman, J. A. C. 4 1991 On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation. Zbl 0707.35141Ablowitz, Mark J.; Herbst, B. M. 56 1990 A numerical study of the nonlinear Schrödinger equation involving quintic terms. Zbl 0685.65110Cloot, A.; Herbst, B. M.; Weideman, J. A. C. 8 1990 On homoclinic boundaries in the nonlinear Schrödinger equation. Zbl 0736.35105Ablowitz, Mark J.; Herbst, B. M. 2 1990 Nonlinear evolution equations, solitons, chaos and cellular automata. Zbl 0728.35102Ablowitz, M. J.; Herbst, B. M.; Keiser, J. M. 2 1990 On numerical chaos in the nonlinear Schrödinger equation. Zbl 0711.35131Herbst, B. M.; Ablowitz, Mark J. 4 1989 A model for the propagation of rounding error in a Klein-Gordon equation. Zbl 0683.65105Cloot, A.; Herbst, B. M. 1 1989 Analytical instability of the Klein-Gordon equation. Zbl 0634.76047Cloot, A. H. J.; Herbst, B. M. 3 1988 Recurrence in semidiscrete approximations of the nonlinear Schrödinger equation. Zbl 0646.65088Weideman, J. A. C.; Herbst, B. M. 5 1987 Split-step methods for the solution of the nonlinear Schrödinger equation. Zbl 0597.76012Weideman, J. A. C.; Herbst, B. M. 107 1986 Accuracy estimates and adaptive refinements in finite element computations. Lectures presented at the international conference held in Lisbon, June 1984. Zbl 0663.65001 44 1986 Numerical experience with the nonlinear Schrödinger equation. Zbl 0589.65084Herbst, B. M.; Morris, J. Ll.; Mitchell, A. R. 26 1985 On the stability of the nonlinear Schrödinger equation. Zbl 0589.65083Herbst, B. M.; Mitchell, A. R.; Weideman, J. A. C. 7 1985 Generalized Petrov-Galerkin methods for the numerical solution of Burgers’ equation. Zbl 0546.65078Herbst, B. M.; Schoombie, S. W.; Griffiths, D. F.; Mitchell, A. R. 9 1984 Equidistributing principles in moving finite element methods. Zbl 0532.65074Herbst, B. M.; Schoombie, S. W.; Mitchell, A. R. 6 1983 A moving Petrov-Galerkin method for transport equations. Zbl 0485.65093Herbst, B. M.; Schoombie, S. W.; Mitchell, A. R. 25 1982 all cited Publications top 5 cited Publications all top 5 Cited by 19 Authors 8 Ma, Wen-Xiu 2 McAnally, Morgan 2 Zhang, Wenying 1 Alipour, Fakhri Y. 1 Boreale, Michele 1 Collodi, Luisa 1 Gu, Xiang 1 Hereman, Willy A. 1 Jhangeer, Adil 1 Khadivar, M. 1 Liu, Yinping 1 Naeem, Imran 1 Poole, Douglas 1 Sapoor, H. 1 Shen, Shoufeng 1 Shi, Changguang 1 Yu, Shuimeng 1 Zhang, Huiqun 1 Zhu, Jiaofeng all top 5 Cited in 11 Serials 3 Applied Mathematics and Computation 2 Journal of Mathematical Physics 2 Journal of Symbolic Computation 2 Communications in Nonlinear Science and Numerical Simulation 1 Physics Letters. A 1 Reports on Mathematical Physics 1 Applied Mathematics Letters 1 Journal of Systems Science and Complexity 1 Journal of Linear and Topological Algebra 1 International Journal of Partial Differential Equations 1 Proceedings of the American Mathematical Society. Series B all top 5 Cited in 8 Fields 13 Partial differential equations (35-XX) 10 Dynamical systems and ergodic theory (37-XX) 3 Computer science (68-XX) 2 Fluid mechanics (76-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Nonassociative rings and algebras (17-XX) 1 Ordinary differential equations (34-XX) 1 Mechanics of particles and systems (70-XX) Citations by Year