All Stories

  1. Numerical quadrature over smooth surfaces with boundaries

    Article • Journal of Computational Physics, February 2018, Elsevier

    Bengt Fornberg, Dr. Jonah A Reeger

  2. A computational exploration of the McCoy–Tracy–Wu solutions of the third Painlevé equation

    Article • Physica D Nonlinear Phenomena, January 2018, Elsevier

    Bengt Fornberg

  3. Methods for the computation of the multivalued Painlevé transcendents on their Riemann surfaces

    Article • Journal of Computational Physics, September 2017, Elsevier

    Bengt Fornberg

  4. Using radial basis function-generated finite differences (RBF-FD) to solve heat transfer equilibrium problems in domains with interfaces

    Article • Engineering Analysis with Boundary Elements, June 2017, Elsevier

    Bengt Fornberg

  5. Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

    Article • Journal of Computational Physics, April 2017, Elsevier

    Bengt Fornberg

  6. On the role of polynomials in RBF-FD approximations: II. Numerical solution of elliptic PDEs

    Article • Journal of Computational Physics, March 2017, Elsevier

    Bengt Fornberg

  7. Stable computations with flat radial basis functions using vector-valued rational approximations

    Article • Journal of Computational Physics, February 2017, Elsevier

    Bengt Fornberg

  8. Fast calculation of Laurent expansions for matrix inverses

    Article • Journal of Computational Physics, December 2016, Elsevier

    Bengt Fornberg

  9. On the role of polynomials in RBF-FD approximations: I. Interpolation and accuracy

    Article • Journal of Computational Physics, September 2016, Elsevier

    Bengt Fornberg

  10. New Directions in Numerical Computation

    Article • Notices of the American Mathematical Society, April 2016, American Mathematical Society (AMS)

    Bengt Fornberg

  11. Numerical Quadrature over the Surface of a Sphere

    Article • Studies in Applied Mathematics, December 2015, Wiley

    Bengt Fornberg, Dr. Jonah A Reeger

  12. A Primer on Radial Basis Functions with Applications to the Geosciences

    Article • September 2015, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  13. A computational overview of the solution space of the imaginary Painlevé II equation

    Article • Physica D Nonlinear Phenomena, August 2015, Elsevier

    Bengt Fornberg

  14. Seismic modeling with radial-basis-function-generated finite differences

    Article • Geophysics, July 2015, Society of Exploration Geophysicists

    Bengt Fornberg

  15. Solving PDEs with radial basis functions

    Article • Acta Numerica, April 2015, Cambridge University Press

    Natasha Flyer, Bengt Fornberg

  16. Fast generation of 2-D node distributions for mesh-free PDE discretizations

    Article • Computers & Mathematics with Applications, April 2015, Elsevier

    Bengt Fornberg

  17. Differentiation: Computation

    Article • January 2015, Springer Science + Business Media

    Bengt Fornberg

  18. Radial Basis Function-Generated Finite Differences: A Mesh-Free Method for Computational Geosciences

    Article • January 2015, Springer Science + Business Media

    Bengt Fornberg

  19. Stability ordinates of Adams predictor-corrector methods

    Article • BIT Numerical Mathematics, December 2014, Springer Science + Business Media

    Bengt Fornberg, Dr. Jonah A Reeger

  20. Seismic modeling with radial basis function-generated finite differences (RBF-FD)

    Article • August 2014, Society of Exploration Geophysicists

    Bengt Fornberg

  21. Painlevé IV: A numerical study of the fundamental domain and beyond

    Article • Physica D Nonlinear Phenomena, July 2014, Elsevier

    Bengt Fornberg, Dr. Jonah A Reeger

  22. Inverting nonlinear dimensionality reduction with scale-free radial basis function interpolation

    Article • Applied and Computational Harmonic Analysis, July 2014, Elsevier

    Bengt Fornberg

  23. Some observations regarding steady laminar flows past bluff bodies

    Article • Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences, June 2014, Royal Society Publishing

    Bengt Fornberg

  24. On spherical harmonics based numerical quadrature over the surface of a sphere

    Article • Advances in Computational Mathematics, April 2014, Springer Science + Business Media

    Bengt Fornberg

  25. Development of meshless computational algorithms for seismic exploration

    Article • August 2013, Society of Exploration Geophysicists

    Bengt Fornberg

  26. A Computational Exploration of the Second Painlevé Equation

    Article • Foundations of Computational Mathematics, May 2013, Springer Science + Business Media

    Bengt Fornberg

  27. A spectrally accurate numerical implementation of the Fokas transform method for Helmholtz-type PDEs

    Article • Complex Variables and Elliptic Equations, April 2013, Taylor & Francis

    Bengt Fornberg

  28. Stable calculation of Gaussian-based RBF-FD stencils

    Article • Computers & Mathematics with Applications, February 2013, Elsevier

    Bengt Fornberg

  29. Radial Basis Function-Generated Finite Differences: A Mesh-Free Method for Computational Geosciences

    Article • January 2013, Springer Science + Business Media

    Bengt Fornberg

  30. Stable Computation of Differentiation Matrices and Scattered Node Stencils Based on Gaussian Radial Basis Functions

    Article • SIAM Journal on Scientific Computing, January 2013, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  31. Painlevé IV with both Parameters Zero: A Numerical Study

    Article • Studies in Applied Mathematics, September 2012, Wiley

    Bengt Fornberg, Dr. Jonah A Reeger

  32. Two Results Concerning the Stability of Staggered Multistep Methods

    Article • SIAM Journal on Numerical Analysis, January 2012, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  33. Radial basis functions: Developments and applications to planetary scale flows

    Article • Computers & Fluids, July 2011, Elsevier

    Bengt Fornberg

  34. A numerical methodology for the Painlevé equations

    Article • Journal of Computational Physics, July 2011, Elsevier

    Bengt Fornberg

  35. Stabilization of RBF-generated finite difference methods for convective PDEs

    Article • Journal of Computational Physics, March 2011, Elsevier

    Bengt Fornberg

  36. Finite difference method

    Article • Scholarpedia, January 2011, Scholarpedia

    Bengt Fornberg

  37. Stable Computations with Gaussian Radial Basis Functions

    Article • SIAM Journal on Scientific Computing, January 2011, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  38. A finite difference method for free boundary problems

    Article • Journal of Computational and Applied Mathematics, April 2010, Elsevier

    Bengt Fornberg

  39. Evolution of solitary waves in a two-pycnocline system

    Article • Journal of Fluid Mechanics, December 2009, Cambridge University Press

    Bengt Fornberg

  40. Comparisons between pseudospectral and radial basis function derivative approximations

    Article • IMA Journal of Numerical Analysis, June 2009, Oxford University Press (OUP)

    Bengt Fornberg

  41. MAGNETIC RELAXATION IN THE SOLAR CORONA

    Article • The Astrophysical Journal, December 2008, Institute of Physics Publishing

    Bengt Fornberg

  42. STEADY VORTEX FLOW PAST A CYLINDER OR SPHERE

    Article • November 2008, World Scientific Pub Co Pte Lt

    Bengt Fornberg

  43. Steady axisymmetric vortex flows with swirl and shear

    Article • Journal of Fluid Mechanics, October 2008, Cambridge University Press

    Bengt Fornberg

  44. Numerical solutions to 2D Maxwell–Bloch equations

    Article • Opto-electronics, April 2008, Springer Science + Business Media

    Bengt Fornberg

  45. On choosing a radial basis function and a shape parameter when solving a convective PDE on a sphere

    Article • Journal of Computational Physics, February 2008, Elsevier

    Bengt Fornberg

  46. A Stable Algorithm for Flat Radial Basis Functions on a Sphere

    Article • SIAM Journal on Scientific Computing, January 2008, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  47. Simulations of 2D Maxwell-Bloch equations

    Article • September 2007, Institute of Electrical & Electronics Engineers (IEEE)

    Bengt Fornberg

  48. The Runge phenomenon and spatially variable shape parameters in RBF interpolation

    Article • Computers & Mathematics with Applications, August 2007, Elsevier

    Bengt Fornberg

  49. Locality properties of radial basis function expansion coefficients for equispaced interpolation

    Article • IMA Journal of Numerical Analysis, March 2007, Oxford University Press (OUP)

    Bengt Fornberg

  50. Stability and accuracy of time-extrapolated ADI-FDTD methods for solving wave equations

    Article • Journal of Computational and Applied Mathematics, March 2007, Elsevier

    Bengt Fornberg

  51. A new class of oscillatory radial basis functions

    Article • Computers & Mathematics with Applications, April 2006, Elsevier

    Bengt Fornberg

  52. Scattered node compact finite difference-type formulas generated from radial basis functions

    Article • Journal of Computational Physics, February 2006, Elsevier

    Bengt Fornberg

  53. A Pseudospectral Fictitious Point Method for High Order Initial‐Boundary Value Problems

    Article • SIAM Journal on Scientific Computing, January 2006, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  54. Stability of vortices in equilibrium with a cylinder

    Article • Journal of Fluid Mechanics, November 2005, Cambridge University Press

    Bengt Fornberg

  55. Magnetic Field Confinement in the Solar Corona. II. Field‐Plasma Interaction

    Article • The Astrophysical Journal, October 2005, Institute of Physics Publishing

    Bengt Fornberg

  56. Accuracy of radial basis function interpolation and derivative approximations on 1-D infinite grids

    Article • Advances in Computational Mathematics, July 2005, Springer Science + Business Media

    Bengt Fornberg

  57. Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions

    Article • Computers & Mathematics with Applications, January 2005, Elsevier

    Bengt Fornberg

  58. Stable computation of multiquadric interpolants for all values of the shape parameter

    Article • Computers & Mathematics with Applications, September 2004, Elsevier

    Bengt Fornberg

  59. Magnetic Field Confinement in the Solar Corona. I. Force‐free Magnetic Fields

    Article • The Astrophysical Journal, May 2004, Institute of Physics Publishing

    Bengt Fornberg

  60. Some unconditionally stable time stepping methods for the 3D Maxwell's equations

    Article • Journal of Computational and Applied Mathematics, April 2004, Elsevier

    Bengt Fornberg

  61. On the Nature of Initial-Boundary Value Solutions for Dispersive Equations

    Article • SIAM Journal on Applied Mathematics, January 2004, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  62. Some observations regarding interpolants in the limit of flat radial basis functions

    Article • Computers & Mathematics with Applications, January 2004, Elsevier

    Bengt Fornberg

  63. A split step approach for the 3-D Maxwell's equations

    Article • Journal of Computational and Applied Mathematics, September 2003, Elsevier

    Bengt Fornberg

  64. A numerical study of some radial basis function based solution methods for elliptic PDEs

    Article • Computers & Mathematics with Applications, September 2003, Elsevier

    Bengt Fornberg

  65. Accurate numerical resolution of transients in initial-boundary value problems for the heat equation

    Article • Journal of Computational Physics, January 2003, Elsevier

    Bengt Fornberg

  66. Interpolation in the limit of increasingly flat radial basis functions

    Article • Computers & Mathematics with Applications, February 2002, Elsevier

    Bengt Fornberg

  67. Observations on the behavior of radial basis function approximations near boundaries

    Article • Computers & Mathematics with Applications, February 2002, Elsevier

    Bengt Fornberg

  68. Some steady axisymmetric vortex flows past a sphere

    Article • Journal of Fluid Mechanics, April 2001, Cambridge University Press

    Bengt Fornberg

  69. Note on Nonsymmetric Finite Differences for Maxwell's Equations

    Article • Journal of Computational Physics, July 2000, Elsevier

    Bengt Fornberg

  70. Some steady vortex flows past a circular cylinder

    Article • Journal of Fluid Mechanics, April 2000, Cambridge University Press

    Bengt Fornberg

  71. Staggered Time Integrators for Wave Equations

    Article • SIAM Journal on Numerical Analysis, January 2000, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  72. A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion

    Article • Journal of Computational Physics, November 1999, Elsevier

    Bengt Fornberg

  73. Steady vortex flows obtained from a nonlinear eigenvalue problem

    Article • ESAIM Proceedings, January 1999, EDP Sciences

    Bengt Fornberg

  74. Block Pseudospectral Methods for Maxwell's Equations II: Two-Dimensional, Discontinuous-Coefficient Case

    Article • SIAM Journal on Scientific Computing, January 1999, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  75. Spatial Finite Difference Approximations for Wave-Type Equations

    Article • SIAM Journal on Numerical Analysis, January 1999, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  76. Large‐scale modeling of ultrasound transducer pulses in lossy, nonlinear tissue

    Article • The Journal of the Acoustical Society of America, September 1998, Acoustical Society of America (ASA)

    Bengt Fornberg

  77. A Practical Guide to Pseudospectral Methods. By B. Fornberg. Cambridge University Press, 1996. 231 pp. ISBN 0 521 49582 2. £37.50.

    Article • Journal of Fluid Mechanics, April 1998, Cambridge University Press

    Bengt Fornberg

  78. A Block Pseudospectral Method for Maxwell's Equations

    Article • Journal of Computational Physics, February 1998, Elsevier

    Bengt Fornberg

  79. On the chance of freak waves at sea

    Article • Journal of Fluid Mechanics, January 1998, Cambridge University Press

    Bengt Fornberg

  80. Classroom Note:Calculation of Weights in Finite Difference Formulas

    Article • SIAM Review, January 1998, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  81. Uses of the Berenger PML in Pseudospectral Methods for Maxwell’s Equations

    Article • January 1998, Springer Science + Business Media

    Bengt Fornberg

  82. Comparison of finite difference- and pseudospectral methods for convective flow over a sphere

    Article • Geophysical Research Letters, December 1997, Wiley

    Bengt Fornberg

  83. A high-order finite-difference method applied to large Rayleigh number mantle convection

    Article • Geophysical & Astrophysical Fluid Dynamics, April 1997, Taylor & Francis

    Bengt Fornberg

  84. A New Numerical Algorithm for the Analytic Continuation of Green's Functions

    Article • Journal of Computational Physics, June 1996, Elsevier

    Bengt Fornberg

  85. A practical guide to pseudospectral methods

    Article • January 1996, Cambridge University Press

    Bengt Fornberg

  86. The prospect for parallel computing in the oil industry

    Article • January 1996, Springer Science + Business Media

    Bengt Fornberg

  87. A Pseudospectral Approach for Polar and Spherical Geometries

    Article • SIAM Journal on Scientific Computing, September 1995, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  88. A compact fourth-order finite difference scheme for the steady incompressible Navier-Stokes equations

    Article • International Journal for Numerical Methods in Fluids, May 1995, Wiley

    Bengt Fornberg

  89. A review of pseudospectral methods for solving partial differential equations

    Article • Acta Numerica, January 1994, Cambridge University Press

    Bengt Fornberg

  90. A finite difference procedure for a class of free boundary problems

    Article • Journal of Computational Physics, September 1992, Elsevier

    Bengt Fornberg

  91. A finite difference procedure for a class of free boundary problems

    Article • Journal of Computational Physics, June 1992, Elsevier

    Bengt Fornberg

  92. FAST GENERATION OF WEIGHTS IN FINITE DIFFERENCE FORMULAS

    Article • March 1992, World Scientific Pub Co Pte Lt

    Bengt Fornberg

  93. Discretization errors at free boundaries of the Grad-Schl�ter-Shafranov equation

    Article • Numerische Mathematik, December 1991, Springer Science + Business Media

    Bengt Fornberg

  94. Steady incompressible flow past a row of circular cylinders

    Article • Journal of Fluid Mechanics, April 1991, Cambridge University Press

    Bengt Fornberg

  95. An improved pseudospectral method for initial-boundary value problems

    Article • Journal of Computational Physics, December 1990, Elsevier

    Bengt Fornberg

  96. High-Order Finite Differences and the Pseudospectral Method on Staggered Grids

    Article • SIAM Journal on Numerical Analysis, August 1990, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  97. Pseudospectral approximation of the elastic wave equation on a staggered grid

    Article • January 1989, Society of Exploration Geophysicists

    Bengt Fornberg

  98. Generation of Finite Difference Formulas on Arbitrarily Spaced Grids

    Article • Mathematics of Computation, October 1988, JSTOR

    Bengt Fornberg

  99. The pseudospectral method: Accurate representation of interfaces in elastic wave calculations

    Article • Geophysics, May 1988, Society of Exploration Geophysicists

    Bengt Fornberg

  100. Steady viscous flow past a sphere at high Reynolds numbers

    Article • Journal of Fluid Mechanics, May 1988, Cambridge University Press

    Bengt Fornberg

  101. Generation of finite difference formulas on arbitrarily spaced grids

    Article • Mathematics of Computation, January 1988, American Mathematical Society (AMS)

    Bengt Fornberg

  102. The pseudospectral method: Comparisons with finite differences for the elastic wave equation

    Article • Geophysics, April 1987, Society of Exploration Geophysicists

    Bengt Fornberg

  103. Steady Viscous Flow Past a Cylinder and a Sphere at High Reynolds Numbers

    Article • January 1987, Springer Science + Business Media

    Bengt Fornberg

  104. The pseudospectral method: Comparisons with finite differences for the elastic wave equation

    Article • January 1986, Society of Exploration Geophysicists

    Bengt Fornberg

  105. Steady viscous flow past a circular cylinder up to reynolds number 600

    Article • Journal of Computational Physics, November 1985, Elsevier

    Bengt Fornberg

  106. A Numerical Method for Conformal Mapping of Doubly Connected Regions

    Article • SIAM Journal on Scientific and Statistical Computing, December 1984, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  107. Numerical Differentiation of Analytic Functions

    Article • ACM Transactions on Mathematical Software, December 1981, ACM (Association for Computing Machinery)

    Bengt Fornberg

  108. Algorithm 579: CPSC: Complex Power Series Coefficients [D4]

    Article • ACM Transactions on Mathematical Software, December 1981, ACM (Association for Computing Machinery)

    Bengt Fornberg

  109. Numerical Computation of Nonlinear Waves

    Article • January 1981, Springer Science + Business Media

    Bengt Fornberg

  110. A Vector Implementation of the Fast Fourier Transform Algorithm

    Article • Mathematics of Computation, January 1981, JSTOR

    Bengt Fornberg

  111. A vector implementation of the Fast Fourier Transform algorithm

    Article • Mathematics of Computation, January 1981, American Mathematical Society (AMS)

    Bengt Fornberg

  112. A Numerical Method for Conformal Mappings

    Article • SIAM Journal on Scientific and Statistical Computing, September 1980, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  113. A numerical study of steady viscous flow past a circular cylinder

    Article • Journal of Fluid Mechanics, June 1980, Cambridge University Press

    Bengt Fornberg

  114. A numerical study of 2-D turbulence

    Article • Journal of Computational Physics, September 1977, Elsevier

    Bengt Fornberg

  115. On a Fourier Method for the Integration of Hyperbolic Equations

    Article • SIAM Journal on Numerical Analysis, September 1975, Society for Industrial & Applied Mathematics (SIAM)

    Bengt Fornberg

  116. Complex zeros of the Jonquière or polylogarithm function

    Article • Mathematics of Computation, May 1975, American Mathematical Society (AMS)

    Bengt Fornberg

  117. Complex Zeros of the Jonquiere or Polylogarithm Function

    Article • Mathematics of Computation, April 1975, JSTOR

    Bengt Fornberg

  118. On the Instability of Leap-Frog and Crank-Nicolson Approximations of a Nonlinear Partial Differential Equation

    Article • Mathematics of Computation, January 1973, JSTOR

    Bengt Fornberg

  119. On the instability of leap-frog and Crank-Nicolson approximations of a nonlinear partial differential equation

    Article • Mathematics of Computation, January 1973, American Mathematical Society (AMS)

    Bengt Fornberg

  120. A method for acceleration of the convergence of infinite series

    Article • BIT Numerical Mathematics, March 1969, Springer Science + Business Media

    Bengt Fornberg

  121. Key properties of PS approximations

    Article • Cambridge University Press

    Bengt Fornberg

  122. Introduction

    Article • Cambridge University Press

    Bengt Fornberg

  123. Preface

    Article • Cambridge University Press

    Bengt Fornberg

  124. PS variations and enhancements

    Article • Cambridge University Press

    Bengt Fornberg

  125. Applications for spectral methods

    Article • Cambridge University Press

    Bengt Fornberg

  126. Jacobi polynomials

    Article • Cambridge University Press

    Bengt Fornberg

  127. Tau, Galerkin, and collocation (PS) implementations

    Article • Cambridge University Press

    Bengt Fornberg

  128. Lebesgue constants

    Article • Cambridge University Press

    Bengt Fornberg

  129. FFT-based implementation of PS methods

    Article • Cambridge University Press

    Bengt Fornberg

  130. Stability domains for some ODE solvers

    Article • Cambridge University Press

    Bengt Fornberg

  131. Energy estimates

    Article • Cambridge University Press

    Bengt Fornberg

  132. References

    Article • Cambridge University Press

    Bengt Fornberg

  133. SCATTERED NODE COMPACT FINITE DIFFERENCE-TYPE FORMULAS GENERATED FROM RADIAL BASIS FUNCTIONS

    Article • Springer Science + Business Media

    Bengt Fornberg

  134. Potential function estimate for polynomial interpolation error

    Article • Cambridge University Press

    Bengt Fornberg

  135. Introduction to spectral methods via orthogonal functions

    Article • Cambridge University Press

    Bengt Fornberg

  136. Introduction to PS methods via finite differences

    Article • Cambridge University Press

    Bengt Fornberg

  137. PS methods in polar and spherical geometries

    Article • Cambridge University Press

    Bengt Fornberg

  138. Comparisons of computational cost for FD and PS methods

    Article • Cambridge University Press

    Bengt Fornberg

  139. Codes for algorithm to find FD weights

    Article • Cambridge University Press

    Bengt Fornberg