Bengt Fornberg | Academic Influence

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Bengt Fornberg

Mathematics

#5827

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#8166

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Applied Mathematics

#172

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#190

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Measure Theory

#965

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#1255

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Mathematics

Bengt Fornberg's Degrees

PhD Applied Mathematics University of Colorado Boulder
Masters Applied Mathematics University of Colorado Boulder
Bachelors Mathematics University of Colorado Boulder

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Bengt Fornberg'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

A practical guide to pseudospectral methods (1996) (1761)
Generation of finite difference formulas on arbitrarily spaced grids (1988) (793)
A numerical study of steady viscous flow past a circular cylinder (1980) (662)
A numerical and theoretical study of certain nonlinear wave phenomena (1978) (657)
A numerical study of some radial basis function based solution methods for elliptic PDEs (2003) (390)
The pseudospectral method: Comparisons with finite differences for the elastic wave equation (1987) (383)
Stable Computations with Gaussian Radial Basis Functions (2011) (381)
Interpolation in the limit of increasingly flat radial basis functions (2002) (346)
Scattered node compact finite difference-type formulas generated from radial basis functions (2006) (340)
The Runge phenomenon and spatially variable shape parameters in RBF interpolation (2007) (329)
Classroom Note: Calculation of Weights in Finite Difference Formulas (1998) (274)
A Stable Algorithm for Flat Radial Basis Functions on a Sphere (2007) (254)
A compact fourth‐order finite difference scheme for the steady incompressible Navier‐Stokes equations (1995) (253)
A primer on radial basis functions with applications to the geosciences (2015) (250)
Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions (2003) (223)
Observations on the behavior of radial basis function approximations near boundaries (2002) (217)
Solving PDEs with radial basis functions * (2015) (216)
On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs (2017) (214)
The pseudospectral method; accurate representation of interfaces in elastic wave calculations (1988) (207)
Numerical Differentiation of Analytic Functions (1981) (205)
On the chance of freak waves at sea (1998) (204)
Steady Viscous Flow Past a Circular Cylinder up to Reynolds Number 600 (1985) (195)
Stable calculation of Gaussian-based RBF-FD stencils (2013) (187)
A split step approach for the 3-D Maxwell's equations (2003) (183)
Some observations regarding interpolants in the limit of flat radial basis functions (2003) (180)
On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy (2016) (178)
Stabilization of RBF-generated finite difference methods for convective PDEs (2011) (177)
Steady viscous flow past a sphere at high Reynolds numbers (1988) (175)
CALCULATION OF WEIGHTS IN FINITE DIFFERENCE FORMULAS∗ (1998) (168)
Radial basis function interpolation: numerical and analytical developments (2003) (167)
On a Fourier method for the integration of hyperbolic equations (1975) (162)
Stable Computation of Multiquadric Interpolants for All Values of the Shape Parameter (2004) (160)
A review of pseudospectral methods for solving partial differential equations (1994) (144)
Stable Computation of Differentiation Matrices and Scattered Node Stencils Based on Gaussian Radial Basis Functions (2013) (140)
Regular Article: A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion (1999) (137)
High-order finite differences and the pseudospectral method on staggered grids (1990) (136)
A numerical study of 2-D turbulence (1977) (133)
On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere (2008) (126)
Some unconditionally stable time stepping methods for the 3D Maxwell's equations (2004) (112)
Staggered Time Integrators for Wave Equations (2000) (110)
A Padé-based algorithm for overcoming the Gibbs phenomenon (2004) (110)
Accuracy of radial basis function interpolation and derivative approximations on 1-D infinite grids (2005) (98)
A Pseudospectral Approach for Polar and Spherical Geometries (1995) (91)
A Numerical Method for Conformal Mappings (1980) (89)
Fast generation of 2-D node distributions for mesh-free PDE discretizations (2015) (81)
On the instability of leap-frog and Crank-Nicolson approximations of a nonlinear partial differential equation (1973) (70)
Steady incompressible flow past a row of circular cylinders (1991) (69)
A numerical methodology for the Painlevé equations (2011) (69)
Stable computations with flat radial basis functions using vector-valued rational approximations (2016) (67)
A new class of oscillatory radial basis functions (2006) (64)
Finite difference method (2011) (62)
Radial basis functions: Developments and applications to planetary scale flows (2011) (60)
Calculations of laminar viscous flow over a moving wavy surface (1982) (53)
Magnetic Field Confinement in the Solar Corona. I. Force-free Magnetic Fields (2004) (52)
Spatial Finite Difference Approximations for Wave-Type Equations (1999) (49)
On the role of polynomials in RBF-FD approximations: III. Behavior near domain boundaries (2019) (48)
A numerical implementation of Fokas boundary integral approach: Laplace's equation on a polygonal domain (2011) (47)
Radial Basis Function-Generated Finite Differences: A Mesh-Free Method for Computational Geosciences (2015) (44)
Seismic modeling with radial-basis-function-generated finite differences (2015) (41)
Block Pseudospectral Methods for Maxwell's Equations II: Two-Dimensional, Discontinuous-Coefficient Case (1999) (40)
A Computational Exploration of the Second Painlevé Equation (2014) (40)
Comparisons between pseudospectral and radial basis function derivative approximations (2010) (39)
Accurate numerical resolution of transients in initial-boundary value problems for the heat equation (2003) (38)
Comparison of finite difference‐ and pseudospectral methods for convective flow over a sphere (1997) (36)
Stability of vortices in equilibrium with a cylinder (2005) (34)
A Block Pseudospectral Method for Maxwell's Equations (1998) (33)
THE GIBBS PHENOMENON FOR RADIAL BASIS FUNCTIONS (2005) (31)
Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals. (2017) (27)
A Pseudospectral Fictitious Point Method for High Order Initial-Boundary Value Problems (2006) (27)
Using radial basis function-generated finite differences (RBF-FD) to solve heat transfer equilibrium problems in domains with interfaces (2017) (26)
Inverting Nonlinear Dimensionality Reduction with Scale-Free Radial Basis Function Interpolation (2013) (24)
Stability and accuracy of time-extrapolated ADI-FDTD methods for solving wave equations (2007) (24)
Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces (2017) (23)
Locality properties of radial basis function expansion coefficients for equispaced interpolation (2007) (22)
On the Fokas method for the solution of elliptic problems in both convex and non-convex polygonal domains (2018) (22)
A Numerical Method for Conformal Mapping of Doubly Connected Regions (1984) (21)
On spherical harmonics based numerical quadrature over the surface of a sphere (2014) (21)
A vector implementation of the Fast Fourier Transform (1981) (21)
Stable computations with Gaussian radial basis functions in 2-D (2009) (21)
A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs (2014) (20)
FAST GENERATION OF WEIGHTS IN FINITE DIFFERENCE FORMULAS (1992) (19)
On spherical harmonics based numerical quadrature over the surface of a sphere (2014) (19)
Some steady vortex flows past a circular cylinder (2000) (19)
Numerical quadrature over smooth, closed surfaces (2016) (19)
Numerical quadrature over smooth surfaces with boundaries (2018) (18)
Painlevé IV with both Parameters Zero: A Numerical Study (2013) (18)
On the Nature of Initial-Boundary Value Solutions for Dispersive Equations (2004) (17)
A high-order finite-difference method applied to large rayleigh number mantle convection (1997) (17)
A practical guide to pseudospectral methods: Applications for spectral methods (1996) (16)
Flow past a row of flat plates at large Reynolds numbers (1993) (16)
Evolution of solitary waves in a two-pycnocline system (2009) (15)
Some steady axisymmetric vortex flows past a sphere (2001) (15)
Fast variable density 3-D node generation (2019) (15)
Transport schemes in spherical geometries using spline-based RBF-FD with polynomials (2020) (13)
Painlevé IV: A numerical study of the fundamental domain and beyond (2014) (13)
Magnetic Field Confinement in the Solar Corona. II. Field-Plasma Interaction (2005) (12)
Stability ordinates of Adams predictor-corrector methods (2015) (12)
Improving the Accuracy of the Trapezoidal Rule (2021) (12)
Steady axisymmetric vortex flows with swirl and shear (2008) (11)
Algorithm 579: CPSC: Complex Power Series Coefficients [D4] (1981) (11)
A Short Proof of the Unconditional Stability of the ADI-FDTD Scheme (2001) (11)
An improved pseudospectral method for fluid dynamics boundary value problems (1990) (11)
Numerical solutions to 2D Maxwell–Bloch equations (2008) (10)
Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces (2017) (9)
Two Results Concerning the Stability of Staggered Multistep Methods (2012) (9)
A finite difference procedure for a class of free boundary problems (1992) (9)
A computational exploration of the McCoy–Tracy–Wu solutions of the third Painlevé equation (2018) (8)
A computational overview of the solution space of the imaginary Painlevé II equation (2015) (8)
Complex Variables and Analytic Functions: An Illustrated Introduction (2019) (8)
Fast high-dimensional node generation with variable density (2017) (8)
MAGNETIC RELAXATION IN THE SOLAR CORONA (2008) (8)
The pseudospectral method : Accurate representation in elastic wave calculations (2001) (8)
Complex zeros of the Jonquière or polylogarithm function (1975) (8)
A practical guide to pseudospectral methods: Comparisons of computational cost for FD and PS methods (1996) (7)
The Radial Basis Functions Method for Improved Numerical Approximations of Geological Processes in Heterogeneous Systems (2019) (7)
Steady viscous flow past a circular cylinder (1984) (7)
Some observations regarding steady laminar flows past bluff bodies (2014) (6)
A finite difference method for free boundary problems (2010) (6)
An improved Gregory-like method for 1-D quadrature (2018) (6)
CPSC : Complex Power Series Coefficients (1973) (5)
Inverting Non-Linear Dimensionality Reduction with Scale-Free Radial Basis Interpolation (2013) (5)
Seismic modeling with radial basis function-generated finite differences (RBF-FD) (2014) (4)
PADÉ-BASED INTERPRETATION AND CORRECTION OF THE GIBBS PHENOMENON (2006) (4)
On the Instability of LeapFrog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation (2007) (4)
Fast calculation of Laurent expansions for matrix inverses (2016) (4)
Contour integrals of analytic functions given on a grid in the complex plane (2020) (4)
Fully numerical Laplace transform methods (2022) (3)
A New Numerical Algorithm for the Analytic Continuation of Green's Functions (1996) (3)
Steady Viscous Flow Past a Cylinder and a Sphere at High Reynolds Numbers (1987) (3)
BIT Numerical Mathematics: Editorial (2005) (3)
3. Boundary Conditions (2012) (3)
Euler–Maclaurin expansions without analytic derivatives (2020) (3)
LOCALIZATION PROPERTIES OF RBF EXPANSION COEFFICIENTS FOR CARDINAL INTERPOLATION (2005) (3)
Solving the Korteweg-de Vries equation with Hermite-based finite differences (2021) (3)
An algorithm for calculating Hermite-based finite difference weights (2020) (3)
Note on Nonsymmetric Finite Differences for Maxwell's Equations (2000) (3)
Explicit Time Stepping of PDEs with Local Refinement in Space-Time (2019) (2)
A method for acceleration of the convergence of infinite series (1969) (2)
Pseudospectral Approximation of the Elastic Wave Equation On a Staggered Grid (1989) (2)
Finite difference formulas in the complex plane (2022) (2)
Steady vortex flows obtained from a nonlinear eigenvalue problem (1999) (2)
Generalizing the trapezoidal rule in the complex plane (2020) (2)
A practical guide to pseudospectral methods: Potential function estimate for polynomial interpolation error (1996) (2)
Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation (1991) (2)
A practical guide to pseudospectral methods: Key properties of PS approximations (1996) (1)
Chapter 1: Brief Summary of Finite Difference Methods (2015) (1)
A practical guide to pseudospectral methods: Preface (1996) (1)
On the Infinite Order Limit of Hermite-based Finite Difference Schemes (2021) (1)
A practical guide to pseudospectral methods: Introduction (1996) (1)
A practical guide to pseudospectral methods: Introduction to spectral methods via orthogonal functions (1996) (1)
Numerical Computation of Nonlinear Waves (1981) (1)
A practical guide to pseudospectral methods: FFT-based implementation of PS methods (1996) (1)
Simulations of 2D Maxwell-Bloch equations (2007) (1)
The Prospect for Parallel Computing in the Oil Industry (1996) (1)
New Directions in Numerical Computation (2016) (1)
Introduction to PS methods via finite differences (1996) (1)
A Monotone Iteration for Steady Axisymmetric Vortex Flows (1999) (0)
A practical guide to pseudospectral methods: Codes for algorithm to find FD weights (1996) (0)
A practical guide to pseudospectral methods: Stability domains for some ODE solvers (1996) (0)
A parallel-in-time approach for wave-type PDEs (2019) (0)
Approximation of the Grad-Schlueter Equation with Free Boundary by Finite Difference (1989) (0)
A practical guide to pseudospectral methods: Jacobi polynomials (1996) (0)
A practical guide to pseudospectral methods: Tau, Galerkin, and collocation (PS) implementations (1996) (0)
A practical guide to pseudospectral methods: PS variations and enhancements (1996) (0)
Training Knowledge and Skills for the Networked Battlefield (2010) (0)
A practical guide to pseudospectral methods: Energy estimates (1996) (0)
Calculations of steady flows past a cylinder and a sphere at finite Re ( a ) Governing equations (2014) (0)
Chapter 3: Introduction to Radial Basis Functions (2015) (0)
Node Subsampling for Multilevel Meshfree Elliptic PDE Solvers (2023) (0)
Chapter 7: RBF-FD Applications to Geo-Modeling: Spherical Domains (2015) (0)
Radial Basis Function-generated Finite Differences : A Mesh-free Method for Computational (2013) (0)
Numerical solutions of the Painlevé equations (2015) (0)
A high-order and mesh-free computational model for non-linear water waves (2019) (0)
Chapter 8: RBF-FD Applications to Geo-Modeling: Limited-Area Domains (2015) (0)
A Computational Exploration of the Second Painlevé Equation (2013) (0)
Scattered Node Mehrstellenverfahren-Type Formulas Generated From Radial Basis Functions (2006) (0)
A practical guide to pseudospectral methods: References (1996) (0)
A practical guide to pseudospectral methods: PS methods in polar and spherical geometries (1996) (0)
Suggested architecture for a specialized fluid dynamics computer (1978) (0)
Chapter 4: Global RBFs for Solving PDEs (2015) (0)
RADIAL BASIS FUNCTIONS - SOME RECENT DEVELOPMENTS (2006) (0)
Numerical Differentiation Functions (1981) (0)
STEADY VORTEX FLOW PAST A CYLINDER OR SPHERE (2008) (0)
Flyer polygonal domain integral approach : Laplace ' s equation on a A numerical implementation of Fokas boundary (2011) (0)
Large‐scale modeling of ultrasound transducer pulses in lossy, nonlinear tissue (1998) (0)
Pseudospectral calculations on 2-D turbulence and nonlinear waves (1978) (0)
AN EFFICIENT AND STABLE HIGH-ORDER TIME STEPPING METHOD FOR THE 3-D MAXWELL ’ S EQUATIONS (0)
Uses of the Berenger PML in Pseudospectral Methods for Maxwell’s Equations (1998) (0)
Numerical quadrature over smooth surfaces with boundaries 1 Numerical quadrature over smooth surfaces with boundaries By (2017) (0)
An improved Gregory-like method for 1-D quadrature (2018) (0)
Chapter 2: Brief Summary of Pseudospectral Methods (2015) (0)
Active topological solitons and transport of cargo in liquid crystals (2018) (0)
Stability of inviscid vortices behind a circular cylinder (2005) (0)
Stability ordinates of Adams predictor-corrector methods (2014) (0)
Chapter 6: Global RBF Applications to Geo-Modeling: Spherical Domains (2015) (0)
Chapter 5: RBF-Generated FD (RBF-FD) Methods (2015) (0)

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