Paul Nelson

Professor Emeritus

Image of Paul Nelson

Research Interests

  • Mathematical software.
  • Numerical analysis
  • Parallel numerical analysis

Awards & Honors

  • Member, IFIP Working Group 14.1
  • Mathematics and Computation Division of the American Nuclear Society, 1980-1991
  • Editor-in-Chief, Marcel Dekker Journal Transport Theory and Statistical Physics,1982-1995.


  • Ph.D Mathematics, University of New Mexico, 1969
  • M.Sc. Physics, University of New Mexico, 1962
  • B.Sc. Engineering Physics, Auburn University, 1958

Selected Publications

"Abstract Riccati Equations in an L1 Space of Finite Measure and Applications to Transport Theory, " Mathematical Methods in the Applied Sciences, Vol. 12, 53-67 (1990).

"An Integrodifferential Equation for the Two-Dimensional Reflection Kernel" (with D. L. Seth), Applied Mathematics and Computation, Vol. 49, 1-18 (1992).

"Global Existence for an Abstract Riccati Initial-Value Problem with Possibly Unbounded Coefficients" (with J. Juang), Journal of Mathematical Analysis and Applications, Vol. 166, 103-111 (1992).

"Error and Optimality for Spatial Approximations in One-Dimensional Transport" (with Fan Yu), Transport Theory and Statistical Physics, Vol. 21, 237-257 (1992).

"Angular Discretization Errors in Transport Theory: An Information-Based Approach," (with Fan Yu), Nuclear Science and Engineering, Vol. 112, 231-238 (1992).

"Existence and Uniqueness of an Inverse Problem for a Hyperbolic System of LIDAR Probing" (with D.D. Bui), Inverse Problems, Vol. 8, 821-829 (1992).

"A Computational Study of Discretization Error in the Solution of the Spencer-Lewis Equation by Doubling Applied to the Upwind Finite-Difference Approximation" (with D.L. Seth, and A..K. Ray), Journal of Computational Physics, Vol. 103, 370-381 (1992).

"LOCFES - A Program for Automatic Determination of the Order of Spatial Approximations in One-Dimensional Particle Transport" (with D.S. Ek), Computer Physics Communications, Vol. 74, 91-118 (1993).

"Worst-Case Errors for Some Spatial Approximations to a Model Problem in Two-Dimensional Transport" (with Transport Theory and Statistical Physics), Vol. 22, 271-291 (1993).

"A Parallel Algorithm for an Inverse Problem Associated with a Hyperbolic System of Partial Differential Equations" (with Mike R. Phillips), Proc. 1994 Int. Conf. Parallel Processing, Vol. III, 55-63 (1994), CRC Press, Inc., Boca Raton, FL.