Bengt Fornberg
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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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(Suggest an Edit or Addition)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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