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## Shizgal, Bernie D.

Compute Distance To:
 Author ID: shizgal.bernie-d Published as: Shizgal, Bernie D.; Shizgal, Bernie; Shizgal, B.; Shizgal, B. D.
 Documents Indexed: 29 Publications since 1981
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#### Co-Authors

 5 single-authored 4 Chen, Heli 4 Jung, Jae-Hun 2 Blackmore, R. 2 Gibelli, Livio 2 Merryfield, William J. 2 Olmos, Daniel 2 Weinert, Ulrich 2 Yang, Henry H. 1 Clarke, Andrew S. 1 Dridi, Raouf 1 Ho, Nicholas 1 Kabin, Konstantin 1 Leung, Ki 1 Lo, Joseph Q. W. 1 Mansell, Gerard 1 Seymour, Brian R. 1 Sospedra-Alfonso, Reinel 1 Su, Yuhong 1 Yang, Xingwei 1 Yau, A. W.
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#### Serials

 7 Journal of Computational Physics 4 Journal of Computational and Applied Mathematics 4 Journal of Mathematical Chemistry 2 Computers and Fluids 2 Computer Methods in Applied Mechanics and Engineering 2 Computer Physics Communications 2 Transport Theory and Statistical Physics 1 Astrophysics and Space Science 1 Computers & Mathematics with Applications 1 Journal of Statistical Physics 1 Mathematics and Computers in Simulation 1 Journal of Scientific Computing
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#### Fields

 21 Numerical analysis (65-XX) 10 Partial differential equations (35-XX) 7 Fluid mechanics (76-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Quantum theory (81-XX) 3 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Biology and other natural sciences (92-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Integral equations (45-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

25 Publications have been cited 309 times in 196 Documents Cited by Year
A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems. Zbl 0459.65096
Shizgal, B.
1981
A pseudospectral method of solution of Fisher’s equation. Zbl 1092.65088
Olmos, Daniel; Shizgal, Bernie D.
2006
Towards the resolution of the Gibbs phenomena. Zbl 1033.65122
Shizgal, Bernie D.; Jung, Jae-Hun
2003
A direct spectral collocation Poisson solver in polar and cylindrical coordinates. Zbl 0951.65125
Chen, Heli; Su, Yuhong; Shizgal, Bernie D.
2000
Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon. Zbl 1053.65102
Jung, Jae-Hun; Shizgal, Bernie D.
2004
Pseudospectral method of solution of the Fitzhugh-Nagumo equation. Zbl 1166.65382
Olmos, Daniel; Shizgal, Bernie D.
2009
A spectral solution of the Sturm-Liouville equation: Comparison of classical and nonclassical basis sets. Zbl 0988.65058
Chen, Heli; Shizgal, Bernie D.
2001
On the numerical convergence with the inverse polynomial reconstruction method for the resolution of the Gibbs phenomenon. Zbl 1117.65176
Jung, Jae-Hun; Shizgal, Bernie D.
2007
A comparison of differential quadrature methods for the solution of partial differential equations. Zbl 0781.65088
Mansell, Gerard; Merryfield, William; Shizgal, Bernie; Weinert, Ulrich
1993
Properties of collocation third-derivative operators. Zbl 0767.65074
Merryfield, William J.; Shizgal, Bernie
1993
A Chebyshev pseudospectral multi-domain method for steady flow past a cylinder, up to Re = 150. Zbl 0817.76064
Yang, Henry H.; Seymour, Brian R.; Shizgal, Bernie D.
1994
A discrete ordinate method of solution of linear boundary value and eigenvalue problems. Zbl 0542.65047
Shizgal, B.; Blackmore, R.
1984
The quadrature discretization method (QDM) in the solution of the Schrödinger equation. Zbl 0916.65089
Chen, Heli; Shizgal, Bernie D.
1998
Chebyshev pseudospectral multi-domain technique for viscous flow calculation. Zbl 0848.76071
Yang, Henry H.; Shizgal, Bernie
1994
Inverse polynomial reconstruction of two dimensional Fourier images. Zbl 1093.65128
Jung, Jae-Hun; Shizgal, Bernie D.
2005
Spectral method based on nonclassical basis functions: The advection-diffusion equation. Zbl 1075.76622
Shizgal, Bernie D.
2002
Pseudospectral methods of solution of the Schrödinger equation. Zbl 1217.81058
Lo, Joseph Q. W.; Shizgal, Bernie D.
2008
Spectral convergence of the Hermite basis function solution of the Vlasov equation: the free-streaming term. Zbl 1189.76406
Gibelli, Livio; Shizgal, Bernie D.
2006
On the generation of orthogonal polynomials using asymptotic methods for recurrence coefficients. Zbl 0773.65005
Clarke, Andrew S.; Shizgal, Bernie
1993
The quadrature discretization method (QDM) in comparison with other numerical methods of solution of the Fokker-Planck equation for electron thermalization. Zbl 0920.65076
Leung, Ki; Shizgal, Bernie D.; Chen, Heli
1998
Suprathermal particle distributions in space physics: Kappa distributions and entropy. Zbl 1206.85027
Shizgal, Bernie D.
2007
Ion energization by wave-particle interactions: comparison of spectral and particle simulation solutions of the Vlasov equation. Zbl 1193.65174
Gibelli, L.; Shizgal, B. D.; Yau, A. W.
2010
The computation of radial integrals with nonclassical quadratures for quantum chemistry and other applications. Zbl 1381.92116
Shizgal, Bernie D.; Ho, Nicholas; Yang, Xingwei
2017
Discrete ordinate solution of a Fokker-Planck equation in laser physics. Zbl 0585.65091
Blackmore, R.; Weinert, U.; Shizgal, B.
1986
Pseudospectral solution of the Fokker-Planck equation with equilibrium bistable states: the eigenvalue spectrum and the approach to equilibrium. Zbl 1354.35159
Shizgal, Bernie D.
2016
The computation of radial integrals with nonclassical quadratures for quantum chemistry and other applications. Zbl 1381.92116
Shizgal, Bernie D.; Ho, Nicholas; Yang, Xingwei
2017
Pseudospectral solution of the Fokker-Planck equation with equilibrium bistable states: the eigenvalue spectrum and the approach to equilibrium. Zbl 1354.35159
Shizgal, Bernie D.
2016
Ion energization by wave-particle interactions: comparison of spectral and particle simulation solutions of the Vlasov equation. Zbl 1193.65174
Gibelli, L.; Shizgal, B. D.; Yau, A. W.
2010
Pseudospectral method of solution of the Fitzhugh-Nagumo equation. Zbl 1166.65382
Olmos, Daniel; Shizgal, Bernie D.
2009
Pseudospectral methods of solution of the Schrödinger equation. Zbl 1217.81058
Lo, Joseph Q. W.; Shizgal, Bernie D.
2008
On the numerical convergence with the inverse polynomial reconstruction method for the resolution of the Gibbs phenomenon. Zbl 1117.65176
Jung, Jae-Hun; Shizgal, Bernie D.
2007
Suprathermal particle distributions in space physics: Kappa distributions and entropy. Zbl 1206.85027
Shizgal, Bernie D.
2007
A pseudospectral method of solution of Fisher’s equation. Zbl 1092.65088
Olmos, Daniel; Shizgal, Bernie D.
2006
Spectral convergence of the Hermite basis function solution of the Vlasov equation: the free-streaming term. Zbl 1189.76406
Gibelli, Livio; Shizgal, Bernie D.
2006
Inverse polynomial reconstruction of two dimensional Fourier images. Zbl 1093.65128
Jung, Jae-Hun; Shizgal, Bernie D.
2005
Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon. Zbl 1053.65102
Jung, Jae-Hun; Shizgal, Bernie D.
2004
Towards the resolution of the Gibbs phenomena. Zbl 1033.65122
Shizgal, Bernie D.; Jung, Jae-Hun
2003
Spectral method based on nonclassical basis functions: The advection-diffusion equation. Zbl 1075.76622
Shizgal, Bernie D.
2002
A spectral solution of the Sturm-Liouville equation: Comparison of classical and nonclassical basis sets. Zbl 0988.65058
Chen, Heli; Shizgal, Bernie D.
2001
A direct spectral collocation Poisson solver in polar and cylindrical coordinates. Zbl 0951.65125
Chen, Heli; Su, Yuhong; Shizgal, Bernie D.
2000
The quadrature discretization method (QDM) in the solution of the Schrödinger equation. Zbl 0916.65089
Chen, Heli; Shizgal, Bernie D.
1998
The quadrature discretization method (QDM) in comparison with other numerical methods of solution of the Fokker-Planck equation for electron thermalization. Zbl 0920.65076
Leung, Ki; Shizgal, Bernie D.; Chen, Heli
1998
A Chebyshev pseudospectral multi-domain method for steady flow past a cylinder, up to Re = 150. Zbl 0817.76064
Yang, Henry H.; Seymour, Brian R.; Shizgal, Bernie D.
1994
Chebyshev pseudospectral multi-domain technique for viscous flow calculation. Zbl 0848.76071
Yang, Henry H.; Shizgal, Bernie
1994
A comparison of differential quadrature methods for the solution of partial differential equations. Zbl 0781.65088
Mansell, Gerard; Merryfield, William; Shizgal, Bernie; Weinert, Ulrich
1993
Properties of collocation third-derivative operators. Zbl 0767.65074
Merryfield, William J.; Shizgal, Bernie
1993
On the generation of orthogonal polynomials using asymptotic methods for recurrence coefficients. Zbl 0773.65005
Clarke, Andrew S.; Shizgal, Bernie
1993
Discrete ordinate solution of a Fokker-Planck equation in laser physics. Zbl 0585.65091
Blackmore, R.; Weinert, U.; Shizgal, B.
1986
A discrete ordinate method of solution of linear boundary value and eigenvalue problems. Zbl 0542.65047
Shizgal, B.; Blackmore, R.
1984
A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems. Zbl 0459.65096
Shizgal, B.
1981
all top 5

#### Cited by 323 Authors

 15 Shizgal, Bernie D. 10 Dehghan Takht Fooladi, Mehdi 8 Gelb, Anne 7 Jung, Jae-Hun 5 Hariharan, Govind 5 Maleki, Mohammad Reza 5 Yun, Beong In 4 Adcock, Ben 4 Hansen, Anders C. 4 Kannan, Krithivasan 4 Li, Benwen 4 Rim, Kyung Soo 4 Wang, Lilian 3 Alici, Haydar 3 Boyd, John Philip 3 Fakhar-Izadi, Farhad 3 Guo, Ben-Yu 3 Kouri, Donald J. 3 Magnus, Alphonse Ph. 3 Mittal, Ramesh Chand 3 Taleei, Ameneh 3 Taşeli, Hasan 3 Wang, Tianjun 2 Abd-Elhameed, Waleed Mohamed 2 Alipanah, Amjad 2 Arora, Geeta 2 Băleanu, Dumitru I. 2 Batenkov, Dmitry 2 Bhrawy, Ali Hassan 2 Cates, Dennis M. 2 Chen, Heli 2 Christlieb, Andrew J. 2 Crampton, Andrew 2 Dağ, İdris 2 Dizicheh, A. Karimi 2 Doha, Eid H. 2 Don, Wai Sun 2 Eliasson, Bengt 2 Greengard, Leslie F. 2 Gröchenig, Karlheinz 2 Hashim, Ishak 2 Hoffman, David K. 2 Jiao, Yujian 2 Jordaan, Kerstin 2 Kajani, M. Tavassoli 2 Kalise, Dante 2 Korkmaz, Alper 2 Kunisch, Karl 2 Li, Weidong 2 Olmos-Liceaga, Daniel 2 Olmos, Daniel 2 Pasquetti, Richard 2 Pataki, Andras 2 Rad, Jamal Amani 2 Sarra, Scott A. 2 Schneider, Kai 2 Shen, Jie 2 Simos, Theodore E. 2 Stefan, Wolfgang 2 Talbot, Chris J. 2 Tanner, Jared W. 2 Teng, Chun-Hao 2 Tribeche, Mouloud 2 Wang, Zhongqing 2 Wei, Guowei 2 Yang, Henry H. 2 Zhang, Desheng 1 Abbasbandy, Saeid 1 Abdi, Ali 1 Abedi, Maryam 1 Ahmadian, Ali 1 Al-Shomrani, Mohammed Mosa 1 Ali, Majid 1 Allouche, Hassane 1 Aly, Emad H. 1 Anh, Vo V. 1 Archibald, Rick 1 Arnold, Mark G. 1 Aslan, Yaşar 1 Atan, Kamel Ariffin Mohd. 1 Balyan, Lokendra K. 1 Barulina, Marina Aleksandrovna 1 Baye, Daniel 1 Benlahsen, Mohammed 1 Berger, Peter 1 Bhatia, Gurpreet Singh 1 Bhatt, Harish P. 1 Bialecki, Bernard 1 Bou-Zeid, Elie 1 Brock, Jerry S. 1 Bürger, Raimund 1 Burrage, Kevin 1 Cao, Junfei 1 Cao, Yong 1 Causley, Matthew F. 1 Cayama, Jorge 1 Cerfon, Antoine J. 1 Chang, Rongyeu 1 Chen, Feng 1 Chen, Qing ...and 223 more Authors
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#### Cited in 57 Serials

 29 Journal of Computational Physics 14 Journal of Scientific Computing 13 Journal of Computational and Applied Mathematics 12 Journal of Mathematical Chemistry 11 Applied Mathematics and Computation 10 Applied Numerical Mathematics 7 Computers & Mathematics with Applications 6 Computer Physics Communications 6 International Journal of Computer Mathematics 5 Mathematics of Computation 5 Mathematics and Computers in Simulation 4 Computers and Fluids 4 Numerical Algorithms 3 Mathematical Methods in the Applied Sciences 3 Journal of Approximation Theory 3 Numerical Methods for Partial Differential Equations 3 Applied Mathematical Modelling 3 Applied and Computational Harmonic Analysis 2 Astrophysics and Space Science 2 Computer Methods in Applied Mechanics and Engineering 2 International Journal for Numerical Methods in Fluids 2 Journal of Fluid Mechanics 2 Transport Theory and Statistical Physics 2 Mathematical and Computer Modelling 2 SIAM Journal on Scientific Computing 2 Engineering Analysis with Boundary Elements 2 The Journal of Fourier Analysis and Applications 2 Nonlinear Dynamics 2 Abstract and Applied Analysis 2 Journal of Applied Mathematics 2 SIAM Journal on Applied Dynamical Systems 2 International Journal for Numerical Methods in Biomedical Engineering 2 Mathematical Sciences 1 International Journal of Engineering Science 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Physics Reports 1 Chaos, Solitons and Fractals 1 International Journal for Numerical Methods in Engineering 1 SIAM Journal on Numerical Analysis 1 Applied Mathematics Letters 1 Physics of Fluids 1 Advances in Computational Mathematics 1 Journal of Vibration and Control 1 Discrete Dynamics in Nature and Society 1 International Journal of Nonlinear Sciences and Numerical Simulation 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 International Journal of Computational Methods 1 Advances in Difference Equations 1 Journal of Statistical Mechanics: Theory and Experiment 1 Random Matrices: Theory and Applications 1 Izvestiya Saratovskogo Universiteta. Novaya Seriya. Seriya Matematika, Mekhanika, Informatika 1 S$$\vec{\text{e}}$$MA Journal 1 East Asian Journal on Applied Mathematics 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 SMAI Journal of Computational Mathematics
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#### Cited in 31 Fields

 150 Numerical analysis (65-XX) 61 Partial differential equations (35-XX) 38 Fluid mechanics (76-XX) 36 Harmonic analysis on Euclidean spaces (42-XX) 13 Ordinary differential equations (34-XX) 13 Statistical mechanics, structure of matter (82-XX) 13 Biology and other natural sciences (92-XX) 12 Special functions (33-XX) 11 Quantum theory (81-XX) 8 Approximations and expansions (41-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 7 Information and communication theory, circuits (94-XX) 5 Integral equations (45-XX) 5 Mechanics of deformable solids (74-XX) 4 Optics, electromagnetic theory (78-XX) 3 Real functions (26-XX) 2 Potential theory (31-XX) 2 Functional analysis (46-XX) 2 Operator theory (47-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Astronomy and astrophysics (85-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Abstract harmonic analysis (43-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)