David I. Gottlieb

David I. Gottlieb's AcademicInfluence.com Rankings

David I. Gottlieb

Computer Science

#4767

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#5032

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Numerical Analysis

#22

World Rank

#23

Historical Rank

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Computer Science

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David I. Gottlieb's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Numerical analysis of spectral methods : theory and applications (1977) (3290)
CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS (1978) (1947)
Spectral methods (2009) (1148)
Numerical analysis of spectral methods (1977) (923)
SPECTRAL METHODS FOR TIME-DEPENDENT PROBLEMS. (2007) (898)
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes (1994) (731)
On the Gibbs Phenomenon and Its Resolution (1997) (729)
A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy (1999) (529)
The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes (1993) (433)
Spectral methods for hyperbolic problems (2001) (314)
Dissipative two-four methods for time-dependent problems (1976) (287)
A Mathematical Analysis of the PML Method (1997) (257)
On the Gibbs phenomenon I: recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function (1992) (252)
The Theoretical Accuracy of Runge-Kutta Time Discretizations for the Initial Boundary Value Problem: A Study of the Boundary Error (1995) (174)
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes (2007) (166)
Optimal time splitting for two- and three-dimensional navier-stokes equations with mixed derivatives (1981) (152)
Regular Article: Well-posed Perfectly Matched Layers for Advective Acoustics (1999) (149)
Spectral Simulations of Electromagnetic Wave Scattering (1997) (149)
A Stable Penalty Method for the Compressible Navier-Stokes Equations: I. Open Boundary Conditions (1996) (148)
Spectral Methods on Arbitrary Grids (1995) (146)
Galerkin method for wave equations with uncertain coefficients (2008) (144)
A new method of imposing boundary conditions in pseudospectral approximations of hyperbolic equations (1988) (133)
On the construction and analysis of absorbing layers in CEM (1998) (131)
Numerical Convergence Study of Nearly Incompressible, Inviscid Taylor–Green Vortex Flow (2005) (130)
Recovering Pointwise Values of Discontinuous Data within Spectral Accuracy (1985) (124)
Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics (2002) (120)
On the Gibbs phenomenon IV: recovering exponential accuracy in a subinterval from a Gegenbauer partial sum of a piecewise analytic function (1995) (113)
The Spectrum of the Chebyshev Collocation Operator for the Heat Equation (1983) (112)
On Numerical Boundary Treatment of Hyperbolic Systems for Finite Difference and Finite Element Methods (1982) (102)
Stable and accurate boundary treatments for compact, high-order finite-difference schemes (1993) (93)
The Chebyshev-Legendre method: implementing Legendre methods on Chebyshev points (1994) (89)
On the direct Fourier method for computer tomography (2000) (87)
Essentially nonoscillatory spectral Fourier methods for shock wave calculations (1989) (84)
Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators (2010) (84)
Uncertainty analysis for the steady-state flows in a dual throat nozzle (2005) (81)
An adaptive pseudo-spectral method for reaction diffusion problems (1989) (79)
On the Gibbs phenomenon III: recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function (1996) (79)
Spectral Methods Based on Prolate Spheroidal Wave Functions for Hyperbolic PDEs (2005) (71)
On the Removal of Boundary Errors Caused by Runge-Kutta Integration of Nonlinear Partial Differential Equations (1994) (68)
The stability of pseudospectral-Chebyshev methods (1981) (68)
Spectral Calculations of One-Dimensional Inviscid Compressible Flows (1981) (63)
Spectral Methods for Discontinuous Problems (1985) (60)
Resolution properties of the Fourier method for discontinuous waves (1994) (59)
The CFL condition for spectral approximations to hyperbolic initial-boundary value problems. (1991) (59)
On the Gibbs phenomenon V: recovering exponential accuracy from collocation point values of a piecewise analytic function (1995) (53)
Spectral Methods for Time-Dependent Problems: Fourier spectral methods (2007) (39)
Boundary conditions for multistep finite-difference methods for time-dependent equations☆ (1978) (38)
The resolution of the Gibbs phenomenon for "spliced" functions in one and two dimensions (1997) (38)
Splitting methods for low Mach number Euler and Navier-Stokes equations (1989) (38)
Strang-Type Difference Schemes for Multidimensional Problems (1972) (36)
Secondary frequencies in the wake of a circular cylinder with vortex shedding (1991) (36)
Spectral Simulation of Supersonic Reactive Flows (1998) (35)
Two-Dimensional Multi-Domain Hybrid Spectral-WENO Methods for Conservation Laws (2006) (35)
Multiple steady states for characteristic initial value problems (1986) (35)
A multidomain spectral method for supersonic reactive flows (2003) (33)
On one-sided filters for spectral Fourier approximations of discontinuous functions (1992) (32)
Numerical stabilizers and computing time for second-order accurate schemes☆ (1972) (31)
Phase Error and Stability of Second Order Methods for Hyperbolic Problems. II (1974) (31)
Cell averaging Chebyshev methods for hyperbolic problems (1992) (30)
On the Optimal Number of Subdomains for Hyperbolic Problems on Parallel Computers (1997) (28)
Stability of pseudospectral and finite-difference methods for variable coefficient problems (1981) (27)
Difference Schemes with Fourth Order Accuracy for Hyperbolic Equations (1974) (27)
Recovering High-Order Accuracy in WENO Computations of Steady-State Hyperbolic Systems (2006) (27)
On the Convergence of the Fourier Approximation for Eigenvalues and Eigenfunctions of Discontinuous Problems (2002) (26)
Parallel pseudospectral domain decomposition techniques (1989) (25)
Spectral simulation of an unsteady compressible flow past a circular cylinder (1990) (23)
The Dufort-Frankel Chebyshev method for parabolic initial boundary value problems (1983) (22)
Collocation methods for the solution of von-Kármán dynamic non-linear plate systems (2004) (22)
Spectral methods for compressible plow problems (1985) (22)
Generalized Du Fort-Frankel methods for parabolic initial-boundary value problems (1976) (22)
Non-Linear PML Equations for Time Dependent Electromagnetics in Three Dimensions (2006) (19)
Topics in spectral methods (1985) (19)
The theoretical accuracy of Runge-Kutta . . . (1997) (18)
Stable spectral methods for conservation laws on triangles with unstructured grids (1999) (18)
Multidimensional Difference Schemes with Fourth-Order Accuracy (1976) (17)
A nonlinear galerkin method: The two-level fourier-collocation case (1995) (17)
High resolution spectral calculations of inviscid compressible flows (1980) (16)
Convergence of spectral methods of hyperbolic initial-boundary value systems (1987) (16)
CONVERGENCE RESULTS FOR PSEUDOSPECTRAL APPROXIMATIONS OF HYPERBOLIC SYSTEMS BY A PENALTY-TYPE BOUNDARY TREATMENT (1991) (16)
EXACT SOLUTION OF A SPIN CHAIN WITH BINARY AND TERNARY INTERACTIONS OF DZIALOSHINSKY-MORIYA TYPE (1999) (16)
On time discretizations for spectral methods (1980) (16)
Explicit characterization of spherical curves (1971) (15)
On the Conservation and Convergence to Weak Solutions of Global Schemes (2003) (15)
A note on the leap-frog scheme in two and three dimensions. [finite difference method for partial differential equations] (1976) (15)
Mathematical Analysis and Optimization of Infiltration Processes (1998) (15)
On the Superconvergence of Galerkin Methods for Hyperbolic IBVP (1996) (14)
Information Content in Spectral Calculations (1985) (14)
On the Navier-Stokes equations with constant total temperature (1976) (14)
Non-oscillatory spectral Fourier methods for shock wave calculations (1988) (14)
Stability of two-dimensional initial-boundary value problems using leap-frog type schemes (1979) (13)
Spectral methods for compressible reactive flows (2005) (13)
Hille-Wintner type oscillation criteria for linear ordinary differential equations of second order (1975) (12)
The reduction of linear ordinary differential equations to equations with constant coefficients (1970) (12)
Stability analysis of intermediate boundary conditions in approximate factorization schemes (1986) (12)
Time Marching Multilevel Techniques for Evolutionary Dissipative Problems (2001) (12)
Spectral methods for time dependent partial differential equations (1983) (11)
Improving the convergence rate to steady state of parabolic ADI methods. [Alternating Direction Implicit (1986) (11)
Optimal Decomposition of the Domain in Spectral Methods for Wave-Like Phenomena (2000) (11)
Improving the convergence rate of parabolic ADI methods (1983) (10)
Spectral Methods for Time-Dependent Problems: Orthogonal polynomials (2007) (10)
Modified Optimal Prediction and its Application to a Particle-Method Problem (2008) (10)
Implementation of the nonlinear Galerkin method with pseudospectral (collocation) discretizations (1993) (10)
Upper and lower bounds on eigenvalues of Sturm-Liouville systems (1971) (10)
Issues in the Application of High Order Schemes (1993) (9)
Higher Order Accuracy Finite Difference Algorithms for Quasi-Linear, Conservation Law Hyperbolic Systems* (1973) (9)
High order methods for complicated flows interacting with shock waves (1997) (7)
ICASE Report No . 924 ICASE ON THE GIBBS PHENOMENON I : RECOVERING EXPONENTIAL ACCURACY FROM THE FOURIER PARTIAL SUM OF A NON-PERIODIC ANALYTIC FUNCTION (7)
On the mathematical analysis and optimization of chemical vapor infiltration in materials science (2000) (7)
On the Stability of the N Cycle Scheme of Lorenz (1974) (6)
Optimization of Chemical Vapor Infiltration with Simultaneous Powder Formation (2000) (6)
General solution for the antiferromagnetic Heisenberg model with exchange anisotropy toward the Ising limit (1991) (5)
ICASE THE CFL CONDITION FOR SPECTRAL APPROXIMATIONS TO HYPERBOLIC INITIAL-BOUNDARY VALUE PROBLEMS (1991) (5)
Quadrature imposition of compatibility conditions in Chebyshev methods (1990) (5)
Domain Decomposition Spectral Approximations for an Eigenvalue Problem with a Piecewise Constant Coefficient (2005) (5)
Singlet excitations in the anisotropic S=1/2 antiferromagnetic Heisenberg model (1992) (5)
Analysis of the Error for Approximations to Systems of Hyperbolic Equations (1999) (4)
On proving stability of multidimensional difference schemes (1975) (4)
Contemporary Mathematics On the Engquist Majda Absorbing Boundary Conditions for Hyperbolic Systems (2005) (4)
Essentially Nonoscillatory Spectral Fourier Method for Shocks Wave Calculations (1989) (4)
Separation of roots and oscillation in ordinary linear differential equations of second order (1971) (4)
Wind Set-down Relaxation on a Sloping Beach (1997) (3)
On the stability of Rusanov's third-order scheme (1974) (3)
Structural instability of a boson system in one dimension (1989) (3)
Magnetoresistance in quasi-one-dimensional compounds (1982) (3)
A Weighted Multi-Domain Spectral Penalty Method with Inhomogeneous Grid for Supersonic Injective Cavity Flows (2009) (3)
Domain Decomposition Survey 143 Methods for Partial Diierential Equationsddm Preconditioner for 4th Order Problems by Using B- Spline Nite Element Method', in Fourth Int. Symp. on Domain Decomposition Methods for Partial Diierential Equationsiterative Substructuring Methods: Algorithms and Theory fo (1994) (3)
The electrical conductivity of very thin metal films (1976) (3)
On time discretizations for spectral methods. [numerical integration of Fourier and Chebyshev methods for dynamic partial differential equations] (1980) (2)
Upper and lower bounds on solutions of initial value problems (1971) (2)
On acceleration of MacCormack's scheme☆ (1978) (2)
On Improving the $2-4$ Two-Dimensional Leap-Frog Scheme (1980) (2)
Analysis of a family of Heisenberg systems with simple eigenfunctions for the ground state and low lying excitations (2005) (2)
15. Survey of Spectral Methods and Applications (1977) (2)
Interplay of holon and spinon dynamics in doped anisotropic Heisenberg chains (1993) (1)
Solutions of problems in nonhomogeneous elasticity (1970) (1)
2. Spectral Methods (1977) (1)
13. Models of Incompressible Fluid Dynamics (1977) (1)
Book Review: High-order methods for incompressible fluid flow@@@Book Review: Lectures on modern convex optimization: analysis, algorithms and engineering applications (2003) (1)
Competition between charge and bond waves in a Peierls-Hubbard model (1990) (1)
Approximate solution of the heisenberg antiferromagnet in a triangular lattice (1993) (1)
Variational solution for the spin 1/2 Heisenberg antiferromagnet with nearest and next nearest neighbor coupling (1992) (1)
ICASE SPECTRAL METHODS FOR TIME DEPENDENT PARTIAL DIFFERENTIAL (2009) (1)
Cell averaging Chebyshev methods for hyperbolic problems. Final report (1990) (1)
Averbuch -parallelizing Implicit Algo- Rithms for Time-dependent Problems by Parabolic Domain Decompositionon the Gibbs Phenomenon I: Recovering Exponential Accuracy from the Fourier Partial Sum of a Non-periodic Analytic Function, 4 Extension on 2-d (1)
Computational Methods for Problems in Aerodynamics and Large Space Structures Using Parallel and Vector Architectures (1987) (0)
A zoo of polynomials (2007) (0)
High Order Accuracy Methods for the Simulations of Reactive Flows (2004) (0)
Foreword (2005) (0)
4. Review of Convergence Theory (1977) (0)
Spectral Methods for Time-Dependent Problems: Trigonometric polynomial approximation (2007) (0)
The Efficient Use of Spectral and Finite Difference Methods for the Solution of Certain Hyperbolic and Parabolic Problems. (1983) (0)
Computational Methods for Problems in Aerodynamics Using Parallel and Vector Architectures (1993) (0)
Transversal magnetoresistance in La2CuO4 (1988) (0)
Proceedings of the fourth international conference on Spectral and high order methods (ICOSAHOM 1998) (2000) (0)
Research in computational fluid dynamics and analysis of algorithms (1992) (0)
Spectral Methods for Time-Dependent Problems: Polynomial expansions (2007) (0)
High Order Accuracy Methods for Supersonic Reactive Flows (2008) (0)
Lattice Unstabilities of Magnetic Origin (1990) (0)
High Order Accuracy Methods for PDEs with Shocks and Uncertainties (2009) (0)
Theory of spectral methods (1985) (0)
Spectral Methods for Time-Dependent Problems: From local to global approximation (2007) (0)
High Order Accuracy Computational Methods in Aerodynamics Using Parallel Architectures (1995) (0)
Figure 1. Convergence of the Arbitrary Grid Legendre Galerkin Method on Various Grids (1995) (0)
ICASE ON THE REMOVAL OF BOUNDARY ERRORS CAUSED BY RUNGE-KUTTA INTEGRATION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS (0)
Corrigendum to "A stable and conservative interface treatment of arbitrary spatial accuracy" [J. Comput. Phys. 148 (1999) 341-365] (2017) (0)
Spectral Methods for Time-Dependent Problems: Stability of polynomial spectral methods (2007) (0)
A VARIATIONAL BETHE-ANSATZ APPROACH TO THE HEISENBERG ANTIFERROMAGNET AT NON-ZERO FIELD (1994) (0)
Equipment for Visualization of Large-Scale Fluid Dynamics Calculations. (1996) (0)
Spectral Methods for Time-Dependent Problems: Bibliography (2007) (0)
U ICASE A STABLE PENALTY METHOD FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS (0)
A Nonlinear Glerkin Method ' The Two-Level Chebyshev Collocation Case (2011) (0)
8. Constant Coefficient Hyperbolic Equations (1977) (0)
9. Time Differencing (1977) (0)
Spectral Methods for Time-Dependent Problems: Discrete stability and time integration (2007) (0)
1. g From finite differences to finite elements: A short history of numerical analysis of partial differential (2003) (0)
Spectral Methods for Time-Dependent Problems: Elements of convergence theory (2007) (0)
High Order Accuracy Computational Methods for Long Time Integration of Nonlinear PDEs in Complex Domains (1998) (0)
Spectral Methods for Time-Dependent Problems: Polynomial approximation theory for smooth functions (2007) (0)
Frustration in a generalized heisenberg chain with Dzialoshinsky-Moriya interactions (2002) (0)
7. Applications of Algebraic-Stability Analysis (1977) (0)
24] G.a. Meurant -a Domain Decomposition Method for Parabolic Problems, Applied (2007) (0)
Parallel Computing Via Multidomain Techniques for Spectral Methods-Abstract (1987) (0)
AFOSR-TR-1-0 3 9 0 THE STABILITY OF PSEUDOSPECTRAL-CHEBYSHEV METHODS (0)
Spectral Methods for Time-Dependent Problems: Polynomial spectral methods (2007) (0)
On acceleration of MacCormack's scheme. [finite difference scheme for hyperbolic and parabolic equations] (1978) (0)
3. Survey of Approximation Theory (1977) (0)
10. Efficient Implementation of Spectral Methods (1977) (0)
14. Miscellaneous Applications of Spectral Methods (1977) (0)
Advances and Challenges in Time-Integration of PDE's (2003) (0)
11. Numerical Results for Hyperbolic Problems (1977) (0)
High-Order Time-Domain Methods for Maxwells Equations (2000) (0)
Transversal Effect in a Metal-to-Metal Interface (1999) (0)
Spatial discretization of the dusty gas equations (2004) (0)
Novel Mathematical and Computational Techniques for Robust Uncertainty Quantification (2011) (0)
ICASE ON THE GIBBS PHENOMENON V : RECOVERING EXPONENTIAL ACCURACY FROM COLLOCATION POINT VALUES OF A PIECEWISE ANALYTIC FUNCTION a . DTIC (0)
Exact electrical conductivity for the t-J model with Dzialoshinsky-Moriya interaction in finite rings (2002) (0)
5. Algebraic Stability (1977) (0)
Spectral Methods for Time-Dependent Problems: Spectral methods for nonsmooth problems (2007) (0)
Spectral methods on general grids (2007) (0)
High Order Methods for the Numerical Simulations of Reactive High Speed Flows (2002) (0)
HIGH ORDER METHODS FOR SUPERSONIC REACTIVE FLOWS AFSOR GRANT FA9550-05-1-0123 FINAL REPORT (2008) (0)
Novel Approaches to the Modeling and Computations of Wave Phenomena (2008) (0)
Numerical Algorithms for Compressible Turbulence. (1997) (0)
Application of Spectral Methods for the Numerical Solution of the Time Dependent Compressible Navier-Stokes Equations. (1978) (0)
12. Advection-Diffusion Equation (1977) (0)
Paired excitations in the antiferromagnetic Heisenberg model with uniaxial anisotropy (1991) (0)
Spectral Methods: Analysis and Applications to Flow Problems. (1986) (0)
6. Spectral Methods Using Fourier Series (1977) (0)
Applications of spectral methods to turbulent magnetofluids in space and fusion research (1984) (0)
On the matrix equations AH + HA∗ = A∗H + HA = I (1977) (0)
Structural instability in a boson system (1990) (0)
Spurious Frequencies as a Result of Numerical Boundary Treatments (1990) (0)

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David I. Gottlieb's Published Works

Published Works

David I. Gottlieb's AcademicInfluence.com Rankings