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Abarbanel, Saul S.

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Author ID: abarbanel.saul-s Recent zbMATH articles by "Abarbanel, Saul S."
Published as: Abarbanel, Saul; Abarbanel, S.; Abarbanel, Saul S.; Abarbanel, S. S.
External Links: MGP
Documents Indexed: 52 Publications since 1961, including 1 Book
Biographic References: 3 Publications

Publications by Year

Citations contained in zbMATH Open

45 Publications have been cited 979 times in 680 Documents Cited by Year
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. Zbl 0832.65098
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
216
1994
The stability of numerical boundary treatments for compact high-order finite-difference schemes. Zbl 0791.76052
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
117
1993
A mathematical analysis of the PML method. Zbl 0887.65122
Abarbanel, Saul; Gottlieb, David
70
1997
The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A study of the boundary error. Zbl 0839.65098
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun
66
1995
Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives. Zbl 0467.76062
Abarbanel, Saul; Gottlieb, David
48
1981
Well-posed perfectly matched layers for advective acoustics. Zbl 0947.76076
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
44
1999
On the construction and analysis of absorbing layers in CEM. Zbl 0924.35160
Abarbanel, Saul; Gottlieb, David
39
1998
Long time behavior of the perfectly matched layer equations in computational electromagnetics. Zbl 1005.78014
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
39
2002
Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I. Zbl 0987.65087
Abarbanel, Saul S.; Chertock, Alina E.
34
2000
Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes. Zbl 0891.65099
Abarbanel, Saul; Ditkowski, Adi
31
1997
Stable and accurate boundary treatments for compact, high-order finite- difference schemes. Zbl 0778.65057
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
26
1993
Compact high-order schemes for the Euler equations. Zbl 0667.76102
Abarbanel, Saul; Kumar, Ajay
22
1988
Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II. Zbl 0987.65088
Abarbanel, Saul S.; Chertock, Alina E.; Yefet, Amir
22
2000
On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations. Zbl 0858.65096
Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.
22
1996
On error bounds of finite difference approximations to partial differential equations. – Temporal behavior and rate of convergence. Zbl 0984.65095
Abarbanel, Saul; Ditkowski, Adi; Gustafsson, Bertil
19
2000
Secondary frequencies in the wake of a circular cylinder with vortex shedding. Zbl 0721.76069
Abarbanel, Saul S.; Don, Wai Sun; Gottlieb, David; Rudy, David H.; Townsend, James C.
13
1991
Splitting methods for low Mach number Euler and Navier-Stokes equations. Zbl 0664.76088
Abarbanel, Saul; Duth, Pravir; Gottlieb, David
13
1989
An iterative finite-difference method for hyperbolic systems. Zbl 0184.52301
Abarbanel, S.; Zwas, G.
13
1969
Spectral methods for discontinuous problems. Zbl 0646.76082
Abarbanel, S.; Gottlieb, D.; Tadmor, E.
13
1986
Numerical solution of quasi-conservative hyperbolic systems - the cylindrical shock problem. Zbl 0243.65071
Abarbanel, S.; Goldberg, M.
12
1972
Multiple steady states for characteristic initial value problems. Zbl 0617.76079
Salas, M. D.; Abarbanel, S.; Gottlieb, D.
12
1986
Long-time performance of unsplit pmls with explicit second order schemes. Zbl 1203.65127
Abarbanel, S.; Qasimov, H.; Tsynkov, S.
11
2009
Non-linear PML equations for time dependent electromagnetics in three dimensions. Zbl 1176.78035
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
10
2006
Bounded error schemes for the wave equation on complex domains. Zbl 1092.65069
Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir
9
2006
Difference schemes with fourth order accuracy for hyperbolic equations. Zbl 0325.65041
Abarbanel, S.; Gottlieb, D.; Turkel, E.
9
1975
Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation. Zbl 0970.76063
Abarbanel, Saul; Ditkowski, Adi
6
1999
Third and fourth order accurate schemes for hyperbolic equations of conservation law form. Zbl 0221.65167
Zwas, Gideon; Abarbanel, Saul
5
1971
Unsplit variables perfectly matched layers for the shallow water equations with Coriolis forces. Zbl 1076.76060
Abarbanel, S.; Stanescu, D.; Hussaini, M. Y.
4
2003
Stability of two-dimensional initial boundary value problems using Leap- Frog type schemes. Zbl 0447.65055
Abarbanel, Saul; Gottlieb, David
4
1979
A note on the leap-frog scheme in two and three dimensions. Zbl 0331.65057
Abarbanel, Saul; Gottlieb, David
4
1976
On proving stability of multidimensional difference schemes. Zbl 0312.65067
Abarbanel, S.; Gottlieb, D.
3
1975
Third and fourth order accuracy schemes for two dimensional hyperbolic equations. Zbl 0263.65087
Zwas, Gideon; Abarbanel, Saul
2
1972
Time dependent temperature distribution in radiating solids. Zbl 0101.31103
Abarbanel, S. S.
2
1961
The motion of shock waves and products of detonation confined between a wall and a rigid piston. Zbl 0165.57804
Abarbanel, S.; Zwas, G.
2
1969
Analysis of the error for approximations to systems of hyperbolic equations. Zbl 0934.65093
Gottlieb, D.; Turkel, E.; Abarbanel, S.
2
1999
Improving the convergence rate to steady state of parabolic ADI methods. Zbl 0608.65055
Abarbanel, Saul S.; Dwoyer, Douglas L.; Gottlieb, David
2
1986
Higher order accuracy finite difference algorithms for quasi-linear, conservation law hyperbolic systems. Zbl 0293.65072
Abarbanel, S.; Gottlieb, D.
2
1973
Stable approximations for hyperbolic systems with moving internal boundary conditions. Zbl 0293.65073
Goldberg, M.; Abarbanel, S.
2
1974
Information content in spectral calculations. Zbl 0642.76085
Abarbanel, Saul; Gottlieb, David
2
1985
Wave propagation in advected acoustics within a non-uniform medium under the effect of gravity. Zbl 1326.76089
Abarbanel, S.; Ditkowski, A.
2
2015
Radiative heat transfer in free-molecule flow. Zbl 0098.17203
Abarbanel, Saul
1
1961
Non-reflecting boundary conditions for compressible Navier-Stokes equations. Zbl 0677.76068
Abarbanel, Saul; Bayliss, Alvin; Lustman, Liviu
1
1986
A semi-implicit scheme for the Navier-Stokes equations. Zbl 0684.76028
Loyd, Bernard; Murman, Earll M.; Abarbanel, Saul S.
1
1988
One dimensional motion of a detonation wave reflecting off a rigid piston. Zbl 0193.56003
Abarbanel, S.
1
1968
Stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes. Zbl 0488.65038
Abarbanel, Saul S.; Murman, Earll M.
1
1982
Wave propagation in advected acoustics within a non-uniform medium under the effect of gravity. Zbl 1326.76089
Abarbanel, S.; Ditkowski, A.
2
2015
Long-time performance of unsplit pmls with explicit second order schemes. Zbl 1203.65127
Abarbanel, S.; Qasimov, H.; Tsynkov, S.
11
2009
Non-linear PML equations for time dependent electromagnetics in three dimensions. Zbl 1176.78035
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
10
2006
Bounded error schemes for the wave equation on complex domains. Zbl 1092.65069
Abarbanel, Saul; Ditkowski, Adi; Yefet, Amir
9
2006
Unsplit variables perfectly matched layers for the shallow water equations with Coriolis forces. Zbl 1076.76060
Abarbanel, S.; Stanescu, D.; Hussaini, M. Y.
4
2003
Long time behavior of the perfectly matched layer equations in computational electromagnetics. Zbl 1005.78014
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
39
2002
Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. I. Zbl 0987.65087
Abarbanel, Saul S.; Chertock, Alina E.
34
2000
Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs. II. Zbl 0987.65088
Abarbanel, Saul S.; Chertock, Alina E.; Yefet, Amir
22
2000
On error bounds of finite difference approximations to partial differential equations. – Temporal behavior and rate of convergence. Zbl 0984.65095
Abarbanel, Saul; Ditkowski, Adi; Gustafsson, Bertil
19
2000
Well-posed perfectly matched layers for advective acoustics. Zbl 0947.76076
Abarbanel, S.; Gottlieb, D.; Hesthaven, J. S.
44
1999
Multi-dimensional asymptotically stable finite difference schemes for the advection-diffusion equation. Zbl 0970.76063
Abarbanel, Saul; Ditkowski, Adi
6
1999
Analysis of the error for approximations to systems of hyperbolic equations. Zbl 0934.65093
Gottlieb, D.; Turkel, E.; Abarbanel, S.
2
1999
On the construction and analysis of absorbing layers in CEM. Zbl 0924.35160
Abarbanel, Saul; Gottlieb, David
39
1998
A mathematical analysis of the PML method. Zbl 0887.65122
Abarbanel, Saul; Gottlieb, David
70
1997
Asymptotically stable fourth-order accurate schemes for the diffusion equation on complex shapes. Zbl 0891.65099
Abarbanel, Saul; Ditkowski, Adi
31
1997
On the removal of boundary errors caused by Runge-Kutta integration of nonlinear partial differential equations. Zbl 0858.65096
Abarbanel, Saul; Gottlieb, David; Carpenter, Mark H.
22
1996
The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A study of the boundary error. Zbl 0839.65098
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul; Don, Wai-Sun
66
1995
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: Methodology and application to high-order compact schemes. Zbl 0832.65098
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
216
1994
The stability of numerical boundary treatments for compact high-order finite-difference schemes. Zbl 0791.76052
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
117
1993
Stable and accurate boundary treatments for compact, high-order finite- difference schemes. Zbl 0778.65057
Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul
26
1993
Secondary frequencies in the wake of a circular cylinder with vortex shedding. Zbl 0721.76069
Abarbanel, Saul S.; Don, Wai Sun; Gottlieb, David; Rudy, David H.; Townsend, James C.
13
1991
Splitting methods for low Mach number Euler and Navier-Stokes equations. Zbl 0664.76088
Abarbanel, Saul; Duth, Pravir; Gottlieb, David
13
1989
Compact high-order schemes for the Euler equations. Zbl 0667.76102
Abarbanel, Saul; Kumar, Ajay
22
1988
A semi-implicit scheme for the Navier-Stokes equations. Zbl 0684.76028
Loyd, Bernard; Murman, Earll M.; Abarbanel, Saul S.
1
1988
Spectral methods for discontinuous problems. Zbl 0646.76082
Abarbanel, S.; Gottlieb, D.; Tadmor, E.
13
1986
Multiple steady states for characteristic initial value problems. Zbl 0617.76079
Salas, M. D.; Abarbanel, S.; Gottlieb, D.
12
1986
Improving the convergence rate to steady state of parabolic ADI methods. Zbl 0608.65055
Abarbanel, Saul S.; Dwoyer, Douglas L.; Gottlieb, David
2
1986
Non-reflecting boundary conditions for compressible Navier-Stokes equations. Zbl 0677.76068
Abarbanel, Saul; Bayliss, Alvin; Lustman, Liviu
1
1986
Information content in spectral calculations. Zbl 0642.76085
Abarbanel, Saul; Gottlieb, David
2
1985
Stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes. Zbl 0488.65038
Abarbanel, Saul S.; Murman, Earll M.
1
1982
Optimal time splitting for two- and three-dimensional Navier-Stokes equations with mixed derivatives. Zbl 0467.76062
Abarbanel, Saul; Gottlieb, David
48
1981
Stability of two-dimensional initial boundary value problems using Leap- Frog type schemes. Zbl 0447.65055
Abarbanel, Saul; Gottlieb, David
4
1979
A note on the leap-frog scheme in two and three dimensions. Zbl 0331.65057
Abarbanel, Saul; Gottlieb, David
4
1976
Difference schemes with fourth order accuracy for hyperbolic equations. Zbl 0325.65041
Abarbanel, S.; Gottlieb, D.; Turkel, E.
9
1975
On proving stability of multidimensional difference schemes. Zbl 0312.65067
Abarbanel, S.; Gottlieb, D.
3
1975
Stable approximations for hyperbolic systems with moving internal boundary conditions. Zbl 0293.65073
Goldberg, M.; Abarbanel, S.
2
1974
Higher order accuracy finite difference algorithms for quasi-linear, conservation law hyperbolic systems. Zbl 0293.65072
Abarbanel, S.; Gottlieb, D.
2
1973
Numerical solution of quasi-conservative hyperbolic systems - the cylindrical shock problem. Zbl 0243.65071
Abarbanel, S.; Goldberg, M.
12
1972
Third and fourth order accuracy schemes for two dimensional hyperbolic equations. Zbl 0263.65087
Zwas, Gideon; Abarbanel, Saul
2
1972
Third and fourth order accurate schemes for hyperbolic equations of conservation law form. Zbl 0221.65167
Zwas, Gideon; Abarbanel, Saul
5
1971
An iterative finite-difference method for hyperbolic systems. Zbl 0184.52301
Abarbanel, S.; Zwas, G.
13
1969
The motion of shock waves and products of detonation confined between a wall and a rigid piston. Zbl 0165.57804
Abarbanel, S.; Zwas, G.
2
1969
One dimensional motion of a detonation wave reflecting off a rigid piston. Zbl 0193.56003
Abarbanel, S.
1
1968
Time dependent temperature distribution in radiating solids. Zbl 0101.31103
Abarbanel, S. S.
2
1961
Radiative heat transfer in free-molecule flow. Zbl 0098.17203
Abarbanel, Saul
1
1961
all top 5

Cited by 900 Authors

70 Nordström, Jan
24 Mattsson, Ken
21 Carpenter, Mark H.
17 Shu, Chi-Wang
17 Zingg, David W.
16 Kreiss, Gunilla
15 Abarbanel, Saul S.
15 Turkel, Eli L.
14 Del Rey Fernández, David C.
13 Svärd, Magnus
12 Hesthaven, Jan S.
10 Hicken, Jason E.
10 Tsynkov, Semyon V.
9 Ditkowski, Adi
9 Duru, Kenneth
9 Gottlieb, David I.
8 Dunham, Eric M.
8 Petersson, N. Anders
8 Wang, Siyang
7 Gassner, Gregor J.
7 Hejranfar, Kazem
7 Hu, Fang Qi
7 Li, Jichun
7 O’Reilly, Ossian
7 Pantano, Carlos
6 Almquist, Martin
6 Bécache, Eliane
6 Berg, Jens
6 Gong, Jing
6 Joly, Patrick
6 Sjogreen, Bjorn
5 Brown, David A.
5 Bruno, Oscar P.
5 Fishelov, Dalia
5 Hagstrom, Thomas M.
5 Hixon, Ray
5 Iaccarino, Gianluca
5 Kim, Jaewook
5 Pullin, Dale I.
5 Ranocha, Hendrik
5 Ruggiu, Andrea Alessandro
5 Tan, Sirui
5 Virta, Kristoffer
4 Barone, Matthew F.
4 Ben-Artzi, Matania
4 Bodony, Daniel J.
4 Boom, Pieter D.
4 Chen, Yaming
4 Corre, Christophe
4 Croisille, Jean-Pierre
4 Deng, Xiaogang
4 Goldberg, Moshe
4 Huang, Yunqing
4 Kachanovska, Maryna
4 Kalashnikova, Irina
4 Kopriva, David Alan
4 Kozdon, Jeremy Edward
4 Kramer, Richard M. J.
4 Lerat, Alain
4 Lundquist, Tomas
4 Minion, Michael L.
4 Müller, Bernhard
4 Nissen, Anna
4 Parseh, Kaveh
4 Werpers, Jonatan
4 Winters, Andrew R.
4 Yamaleev, Nail K.
4 Yefet, Amir
4 Zhang, Mengping
4 Zhong, Xiaolin
4 Zwas, Gideon
3 Appelö, Daniel
3 Baeza, Antonio
3 Barucq, Hélène
3 Chertock, Alina E.
3 Colonius, Tim
3 Coulombel, Jean-François
3 Deng, Shaozhong
3 Doostan, Alireza
3 Erickson, Brittany A.
3 Eriksson, Sofia
3 Fisher, Travis C.
3 Gaitonde, Datta V.
3 Gerritsen, Margot G.
3 Ghasemi, Fatemeh
3 Gustafsson, Bertil
3 Halpern, Laurence
3 Ham, Frank E.
3 Kallivokas, Loukas F.
3 Li, Tingting
3 Li, Xiaodong
3 Linders, Viktor
3 Mellado, Juan Pedro
3 Mulet, Pep
3 Nikkar, Samira
3 Olsson, Pelle
3 Parsani, Matteo
3 Pettersson, Per
3 Prieto, Andrés
3 Pruett, C. David
...and 800 more Authors
all top 5

Cited in 86 Serials

254 Journal of Computational Physics
86 Journal of Scientific Computing
43 Computers and Fluids
30 Applied Numerical Mathematics
19 Journal of Computational and Applied Mathematics
15 Computer Methods in Applied Mechanics and Engineering
14 Mathematics of Computation
14 SIAM Journal on Scientific Computing
13 Computers & Mathematics with Applications
13 Journal of Fluid Mechanics
11 Applied Mathematics and Computation
9 International Journal for Numerical Methods in Fluids
9 International Journal for Numerical Methods in Engineering
7 BIT
7 International Journal of Computational Fluid Dynamics
6 Numerische Mathematik
6 SIAM Journal on Numerical Analysis
6 Physics of Fluids
5 Numerical Methods for Partial Differential Equations
5 Mathematical and Computer Modelling
5 Journal of Computational Acoustics
5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
4 Wave Motion
4 Theoretical and Computational Fluid Dynamics
3 Journal of Engineering Mathematics
3 International Journal of Computer Mathematics
3 International Journal of Numerical Methods for Heat & Fluid Flow
3 Advances in Computational Mathematics
3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
2 Computer Physics Communications
2 General Relativity and Gravitation
2 Journal of Statistical Physics
2 Applied Mathematics and Mechanics. (English Edition)
2 Physica D
2 RAIRO. Modélisation Mathématique et Analyse Numérique
2 Computational Mechanics
2 COMPEL
2 Numerical Algorithms
2 Applied Mathematical Modelling
2 Journal de Mathématiques Pures et Appliquées. Neuvième Série
2 Linear Algebra and its Applications
2 Computational Geosciences
2 Archives of Computational Methods in Engineering
2 International Journal of Advances in Engineering Sciences and Applied Mathematics
2 AMM. Applied Mathematics and Mechanics. (English Edition)
1 Acta Mechanica
1 Archive for Rational Mechanics and Analysis
1 Astrophysics and Space Science
1 Classical and Quantum Gravity
1 Journal of Mathematical Analysis and Applications
1 Journal of Mathematical Physics
1 Mathematical Biosciences
1 Mathematical Notes
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Physics of Fluids, A
1 Calcolo
1 Mathematics and Computers in Simulation
1 Quarterly of Applied Mathematics
1 Studies in Applied Mathematics
1 Applied Mathematics Letters
1 Science in China. Series A
1 Archive of Applied Mechanics
1 Computational and Applied Mathematics
1 Discrete and Continuous Dynamical Systems
1 Journal of Vibration and Control
1 Vietnam Journal of Mathematics
1 Journal of Shanghai University
1 International Journal of Numerical Modelling
1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
1 Communications in Nonlinear Science and Numerical Simulation
1 Optimization and Engineering
1 Living Reviews in Relativity
1 Journal of Nonlinear Mathematical Physics
1 Mathematical Modelling and Analysis
1 Foundations of Computational Mathematics
1 Discrete and Continuous Dynamical Systems. Series B
1 Computational Methods in Applied Mathematics
1 International Journal of Numerical Methods and Applications
1 Symmetry
1 S\(\vec{\text{e}}\)MA Journal
1 SIAM/ASA Journal on Uncertainty Quantification
1 Journal de l’École Polytechnique – Mathématiques
1 Séminaire Laurent Schwartz. EDP et Applications
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys
1 SN Partial Differential Equations and Applications
1 Results in Applied Mathematics

Citations by Year