Dr. Edward J. Allen

Professor Emeritus
Department of
Mathematics and Statistics
Texas Tech University
Lubbock, Texas 79409-1042


E-mail: edward.allen@ttu.edu


Welcome to the home page of Edward J. Allen at Texas Tech University , Department of Mathematics and Statistics.

Research Interests

Numerical analysis, Stochastic differential equations, Mathematical modeling

Education

  1. Ph.D., Mathematics, University of Tennessee, Knoxville, August, 1983.
  2. M.S., Nuclear Engineering, University of Wisconsin, Madison, December, 1972.
  3. B.S., Nuclear Engineering, University of Wisconsin, Madison, August, 1971.

Professional Experience

  1. Professor, Department of Mathematics and Statistics, Texas Tech University,  1998-present.
  2. Associate Professor, Department of Mathematics, Texas Tech University, 1991-1998.
  3. Assistant Professor, Department of Mathematics, Texas Tech University, 1985-1991.
  4. Assistant Professor, Department of Mathematics, University of North Carolina at Asheville, 1982-1985.
  5. Nuclear Engineer, Oak Ridge National Laboratory, Oak Ridge, Tennessee, 1974-1980.

Graduate Work Directed

  1. William E. Abbott, M.S., Thesis: Richardson extrapolation of a positive method for numerically solving the transport equation in spherical geometry, May, 1989.
  2. Tai Fu T. Yang, M.S., Report: Study of mesh rebalance acceleration for neutron transport in plane geometry, August, 1989.
  3. J. M. Harris, M.A., Report: Persistence-time models for use in viability analysis of vanishing species, August, 1990.
  4. Chian-Chian Du (Melody Stamp), M.S., Thesis: Richardson extrapolation applied to nonlinear functional equations, May, 1991.
  5. Sally Goodlett, M.S., Thesis: Extrapolation of numerical methods for solving stochastic differential equations, May, 1992.
  6. Like Liu, M.S., Thesis: A semidiscrete Galerkin method for numerical solution of the one-dimensional periodic Vlasov-Poisson equation and comparison with the particle method, May, 1993.
  7. Paul Pierce, M.S., Thesis: Efficient eigenvalue computation for nonnegative irreducible matrices, co-advisor: H. D. Victory, Jr., May, 1994.
  8. Sudasanna Ponweera, M.S., Report: Analysis of weed dispersal on rangeland, co-advisor: L. J. S. Allen , December, 1994.
  9. Marwan Abukhaled. Ph.D., Dissertation: Development and analysis of Runge-Kutta and recursive distribution numerical methods for approximate solution of stochastic differential equations, May, 1995.
  10. S. J. Novosel, M.S., Thesis: Spectral and discrete approximations to stochastic Fredholm integral equations, May, 1996.
  11. W. D. Sharp, M.S., Thesis: Numerical solution of first passage time problems, December, 1996.
  12. M. Chowdhury, M.S., Thesis: A stochastic age-structured population model, May 1998.
  13. K. Boyd, M.S., Thesis: Numerical methods for approximation of square roots of positive definite matrices in matrix-vector products, May, 1999.
  14. W. D. Sharp, Ph.D., Dissertation: Derivation of stochastic neutron transport equations and numerical analysis of stochastic Volterra population equations, May, 1999.
  15. M. Shubov, M.S.(physics), Thesis: A feasibility study of an accelerator driven nuclear energy system, co-advisor: M. Lodhi (physics), December, 2000.
  16. R. M. Berry, M.S., Thesis: An inverse power method for approximation of multiplication factors in neutron transport, May, 2001.
  17. J. Severino, M.S., Thesis: Acceleration of quasi-Monte Carlo approximations with applications to financial mathematics, May, 2001.
  18. C. Thompson, M.S., Thesis: A Stochastic Differential Equation Model for Charged-Particle Energy Straggling, August, 2001.
  19. Armando Arciniega Ph. D., Dissertation: Richardson extrapolation of difference methods in financial option valuation and the development and analysis of shooting methods for Stratonovich stochastic differential equation systems with boundary conditions, August 2003.
  20. K. Johnson, M.S., Thesis: A computational investigation on the effects of rounding errors in least squares estimation with applications to financial mathematics, co-advisor: H. D. Victory, Jr., May, 2002.
  21. M. Kinard, M.S., Thesis: Computational solution of the point kinetics equations in nuclear reactor dynamics, Expected completion date December, 2003.
  22. I. Martines, M.S., Thesis: Efficient numerical solution of functions of matrices, May, 2004.
  23. T. Hopkins, M.S., Thesis: Numerical solution of stochastic delay integrodifferential equations in population dynamics, May, 2004.
  24. J. Hayes, M.S., Thesis: Derivation and computational solution of stochastic point kinetics equations in nuclear reactor dynamics, May, 2005.
  25. A. Drew, M.S., Thesis: An investigation of climatic and geographic factors on the growth and spread of Chytrid fungus on amphibian populations in Australia, co-advisor: L. J. S. Allen, December, 2004.
  26. R. Koskodan, Ph.D., Dissertation: Extrapolation of implicit numerical methods for stochastic differential equations and development of a stock-price model with application to multi-asset option pricing, August, 2006.
  27. H. Simsek, M.S., Thesis: Stochastic and Monte Carlo Models For Fiber Breakage in Cotton Processing, co-advisor: Mourad Krifa, May, 2007.
  28. C. Huff, M.S., Thesis: Derivation of a Stochastic Differential Equation Model for Sunspot Activity, December, 2009.
  29. E. Dogan, M.S., Report: Derivation and Application of Stochastic Partial Differential Equations for Reaction-Diffusion Systems, August, 2010.
  30. U. Bulut, M.S., Report: Derivation of a Stochastic Telegraph Equation, August, 2010.
  31. E. Dogan, Ph.D., Dissertation: Derivation and Application of Stochastic Partial Differential Equations for Reaction-Diffusion Processes and Stochastic Differential Equations for Alleles, August, 2011.
  32. U. Bulut, Ph.D., Dissertation: Derivation and Application of Stochastic Correlated Random-Walk Models and Stochastic Differential Equations in Phylogenetics, December, 2013.

Teaching Recognitions

  1. Named Outstanding Texas Tech Mathematics Teacher for 1988-1989 by Kappa Mu Epsilon Mathematics Honor Society.
  2. Named Texas Tech Mathematics Graduate Professor for 2002-2003 by the Texas Tech University Chapter of the Society of Industrial and Applied Mathematics.
  3. Named Professor of the Year for 2013 by Kappa Mu Epsilon Mathematics Honor Society.

Publications

1.      E. J. Allen and C. W. Maynard, 14 MeV Neutron Collimator Design for Cancer Therapy , Transactions of the American Nuclear Society, 19, 48 (1974).

2.      E. J. Allen and H. T. Kerr, Neutron Flux Computational Model of the Oak Ridge Research Reactor , Transactions of the American Nuclear Society, 21, 461-462 (1975). (See also ORNL-TM-4814.)

3.      E. J. Allen, CACA-2: A Revised Version of CACA - A Heavy Isotope and Fission Product  Concentration Calculational Code for Experimental Irradiation Capsules, ORNL/TM-5266, (February, 1976). (See also RSIC Code Package CCC-302, Radiation Safety Information Computational Center RSICC Number C00302 I0360 00.)

4.      E. J. Allen, H. T. Kerr, and J. F. Mincey, Instruments for Measurement of In-Core Nuclear Heating Rates , Transactions of the American Nuclear Society, 26, 605-606 (1977).

5.      E. J. Allen, J. E. Rushton, M. M. Chiles, and J. D. Jenkins, Evaluation of a Nondestructive Assay Technique for On-Line Assay of Fuel Rods in an HTGR Fuel Refabrication Plant , Transactions of the American Nuclear Society, 33 , 441-442 (1979). (See also ORNL-TM-6960.)

6.      E. J. Allen and S. R. McNeany, Nondestructive Fissile Isotopic Measurement Technique for Uranium-233 - Uranium-235 Fuels Using Prompt and Delayed Fission Neutron Counting , Nuclear Technology, 47, 363-377 (1980).

7.      E. J. Allen, An Application of Global Approximations in the Finite Element Method , International Journal for Numerical Methods in Engineering, 21, 1749-1758 (1985).

8.      E. J. Allen, Continued Radicals, , The Mathematical Gazette, 69, 261-263 (1985).

9.      E. J. Allen, A Finite Element Approach for Treating the Energy Variable in the Numerical Solution of the Neutron Transport Equation , Transport Theory and Statistical Physics, 15, 449-478 (1986).

10.  E. J. Allen, On the Error in Pade Approximation , SIAM Review (problem section), 30, 319-320 (1988).

11.  H. D. Victory, Jr. and E. J. Allen, On the Convergence of the Multigroup Discrete Ordinates Solutions for Subcritical Transport Media , Annali di Matematica pura ed applicata, CLIII, 229-274 (1988).

12.  E. J. Allen, Application of Richardson Extrapolation to Numerical Solution of the Neutron Transport Equation , Nuclear Science and Engineering, 99, 123-132 (1988).

13.  E. J. Allen, H. D. Victory, Jr., and K. Ganguly, On the Convergence of Finite-Differenced Multigroup, Discrete-Ordinates Methods for Anisotropically Scattering Slab Media , SIAM Journal on Numerical Analysis, 26, 88-106 (1989).

14.  E. J. Allen, Richardson Extrapolation of the Step-Characteristic Method in Rectangular Geometry , Annals of Nuclear Energy, 16, 159-172 (1989).

15.  J. T. White, E. Allen, K. Ganguly, L. Schovanec, An Efficient Algorithm for Calculating Taylor Polynomials of Implicit Functions , International Journal of Computer Mathematics, 31, 137-145 (1990).

16.  H. D. Victory, Jr. and E. J. Allen, The Convergence Theory of Particle-in-Cell Methods for Vlasov-Poisson Systems , SIAM Journal on Numerical Analysis, 28, 1207-1241 (1991).

17.  K. Ganguly, E. J. Allen, and H. D. Victory, Jr., A New Approach to Neutron Transport , Transport Theory and Statistical Physics, 20, 3-29 (1991).

18.  W. E. Abbott and E. J. Allen, Richardson Extrapolation Applied to Difference Methods for Numerically Solving the Neutron Transport Equation in Spherical Geometry , Nuclear Science and Engineering, 108, 278-288 (1991).

19.  L. J. S. Allen, E. J. Allen, C. R. G. Kunst, and R. E. Sosebee, A Diffusion Model for Dispersal of Opuntia Imbricata (Cholla) on Rangeland , Journal of Ecology, 79,1123-1135 (1991).

20.  E. J. Allen, J. M. Harris, and L. J. S. Allen, Persistence-Time Models For Use In Viability Analyses of Vanishing Species , Journal of Theoretical Biology, 155, 33-53 (1992).

21.  K. Ganguly, G. Tucker, E. J. Allen, H. D. Victory, Jr., SNCONV Computer Code Abstract , Nuclear Science and Engineering, 110, 205-206 (1992).

22.  F. A. Mohamed, E. J. Allen, and K. Rainwater, Well Response Tests: III. The Inverse Problem, Inverse Problems, 9, 483-493 (1993).

23.  E. J. Allen, Requirements for Long-Term Persistence of the Texas Horned Lizard, Phrynosomatics, pg.2,5 (August/September 1993).

24.  E. J. Allen, Application of Richardson Extrapolation to Linear Functional Equations with Mildly Smooth Solutions , International Journal of Computer Mathematics, 47, 239-250 (1993).

25.  E. J. Allen and H. D. Victory, Jr., Random Particle Method for Numerical Solution of the VPFP Equations , Transactions of the American Nuclear Society, 69, 233-234 (1993).

26.  E. J. Allen and H. D. Victory, Jr., A Computational Investigation of the Random Particle Method for Numerical Solution of the Kinetic Vlasov-Poisson-Fokker-Planck Equations , Physica A, 209, 318-346 (1994).

27.  S. T. Goodlett and E. J. Allen, A Variance Reduction Technique For Use With the Extrapolated Euler Method for Numerical Solution of Stochastic Differential Equations , Stochastic Analysis and Applications, 12, 131-140 (1994).

28.  E. J. Allen, International Harvesters, Texas Parks and Wildlife, 36-37 (July 1995).

29.  E. J. Allen and C. J. Nunn, Difference Methods for Numerical Solution of Stochastic Two-Point Boundary-Value Problems , Proceedings of the First International Conference on Difference Equations, S. N. Elaydi, J. R. Graef, G. Ladas, A. C. Peterson (editors), Gordon and Breach Publishers, Amsterdam (1995).

30.  E. J. Allen, L. J. S. Allen, and X. Gilliam, Dispersal and Competition Models for Plants, Journal of Mathematical Biology, 34, 455-481 (1996).

31.  E. J. Allen, Harvester Ants: Specialists in Plant Seeds, New Mexico Wildlife, 22-23 (January/February 1996).

32.  L. J. S. Allen, E. J. Allen, and S. Ponweera, A Mathematical Model for Weed Dispersal and Control , Bulletin of Mathematical Biology, 58, 815-834 (1996).

33.  M. I. Abukhaled and E. J. Allen, A Class of Second-Order Runge-Kutta Methods for Numerical Solution of Stochastic Differential Equations , Stochastic Analysis and Applications, 16, 977-991 (1998).

34.  M. I. Abukhaled and E. J. Allen, A Recursive Integration Method For Approximate Solution of Stochastic Differential Equations , International Journal of Computer Mathematics , 66, 53-66 (1998).

35.  E. J. Allen, S. J. Novosel, Z. Zhang, Finite Element and Difference Approximation of Some Linear Stochastic Partial Differential Equations , Stochastics, 64, 117-142 (1998).

36.  W. D. Sharp and E. J. Allen, Numerical Solution of First Passage Time Problems Using An Approximate Chapman-Kolmogorov Relation , Probabilistic Engineering Mechanics, 13, 233-241 (1998).

37.  L. J. S. Allen and E. J. Allen, Mathematical models for the dispersal and control of undesirable plants on rangeland, Proceedings of the Fifth International Conference on Desert Development: The Endless Frontier. Vol. 1, 488-503 (1999).

38.  E. J. Allen, Stochastic differential equations and persistence time of two interacting populations , Dynamics of Continuous, Discrete, and Impulsive Systems, 5, 271-281 (1999).

39.  L. J. S. Allen, E. J. Allen, and D. N. Atkinson, Integrodifference equations applied to plant dispersal , competition, and control , Proceedings of the International Conference on Differential Equations with Applications to Biology, Fields Institute Communications, 21, 15-30 (1999).

40.  W. D. Sharp and E. J. Allen, Stochastic neutron transport equations for rod and plane geometries , Annals of Nuclear Energy, 27, 99-116 (2000).

41.  E. J. Allen, J. Baglama, and S. K. Boyd, Numerical approximation of the product of the square root of a matrix with a vector , Linear Algebra and its Applications, 310, 167-181 (2000).

42.  E. J. Allen, Requirements for Long-Term Persistence of the Texas Horned Lizard, Phrynosomatics, (Special 10th Anniversary Issue), 10-11 (December 2000).

43.  E. J. Allen, Random selection of 3-digit numbers , Mathematical Spectrum, 33, 8-10 (2000/2001).

44.  M. Chowdhury and E. J. Allen, A stochastic continuous-time age-structured population model, Nonlinear Analysis, 47, 1477-1488 (2001).

45.  Marwan Abukhaled and Edward J. Allen, Expectation stability of second-order weak numerical methods for stochastic differential equations, Stochastic Analysis and Applications, 20, 693-707 (2002).

46.  E. J. Allen and R. M. Berry, The inverse power method for calculation of multiplication factors, Annals of Nuclear Energy, 29, 929-935 (2002).

47.  Edward Allen, John Burns, David Gilliam, Joe Hill, and Victor Shubov, The impact of finite precision arithmetic and sensitivity on the numerical solution of partial differential equations, Mathematical and Computer Modeling, 35, 1165-1195 (2002).

48.  E. J. Allen and H. D. Victory, Jr., A stochastic continuous model for schistosomiasis, Proceedings of Neural, Parallel, and Scientific Computations , Editors: M. P. Bekakos, G. S. Ladde, N. G. Medhin, and M. Sambandham, Volume 2, 71-74 (2002).

49.  E. J. Allen and C. M. Thompson, A stochastic differential equation model for charged-particle energy straggling, Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms 10,19-27 (2003).

50.  Armando Arciniega and Edward Allen, Rounding error in numerical solution of stochastic differential equations, Stochastic Analysis and Applications, 21, 281-300 (2003).

51.  Wyatt D. Sharp and Edward J. Allen, Development and Analysis of Quadrature and Galerkin Methods for Approximate Solution to the Integral Formulation of Volterra's Population Equation with Diffusion and Noise, International Journal of Pure and Applied Mathematics, 4, 457-486 (2003).

52.  E. J. Allen and H. D. Victory, Jr., Modelling and simulation of a schistosomiasis infection with biological control, Acta Tropica, 87, 251-267 (2003).

53.  Armando Arciniega and Edward Allen, Extrapolation of difference methods in option valuation, Applied Mathematics and Computation, 153, 165-186 (2004).

54.  Armando Arciniega and Edward Allen, Shooting methods for numerical solution of stochastic boundary-value problems, Stochastic Analysis and Applications, 22, 1-20 (2004).

55.  L. J. S. Allen and E. J. Allen, A comparison of three different stochastic population models with regard to persistence time, Theoretical Population Biology, 68, 439-449 (2003).

56.  J. S. Severino, E. J. Allen, H. D. Victory, Jr., Acceleration of quasi-Monte Carlo approximations with applications in mathematical finance, Applied Mathematics and Computation, 148, 173-187 (2004).

57.  M. Kinard and E. J. Allen, Efficient numerical solution of the point kinetics equations in nuclear reactor dynamics, Annals of Nuclear Energy, 31, 1039-1051 (2004).

58.  Edward J. Allen, Jump-diffusion model for the global spread of an amphibian disease, International Journal of Numerical Analysis and Modeling, 1, 173-187 (2004).

59.  Edward J. Allen, Linda J. S. Allen, Henri Schurz, A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability, Mathematical Biosciences, 196, 14-38 (2005).

60.  J. G. Hayes and E. J. Allen, Stochastic point-kinetics equations in nuclear reactor dynamics, Annals of Nuclear Energy, 32, 572-587 (2005).

61.  Rachel Koskodan and Edward Allen, Extrapolation of the stochastic theta numerical method for stochastic differential equations, Stochastic Analysis and Applications, 24, 475-487 (2006).

62.  L. J. S. Allen, E. J. Allen, and C. B. Jonsson, The impact of environmental variation on hantavirus infection in rodents, AMS Contemporary Mathematics Series, C. Castillo-Chavez, D. P. Clemence, and A. B. Gumel, Eds., Proceedings of the Joint Summer Research Conference on Modeling the Dynamics of Human Diseases: Emerging Paradigms and Challenges, Vol. 410, 1-16 (2006).

63.  A. Drew, E. J. Allen, and L. J. S. Allen, Analysis of Climatic and Geographic Factors on the Presence of Chytridiomycosis in Australia, Diseases of Aquatic Organisms, 68, 245-250 (2006).

64.  Edward Allen, Ali Khoujmane, Mourad Krifa, Hakan Simsek, A stochastic differential equation model for cotton fiber breakage, Neural, Parallel and Scientific Computations, 15, 181-192 (2007).

65.  E. J. Allen, L. J. S. Allen, A. Arciniega, P. Greenwood, Construction of equivalent stochastic differential equation models, Stochastic Analysis and Applications, 26, 274-297 (2008).

66.  Rachel Koskodan and Edward Allen, Construction of consistent discrete and continuous stochastic models for multiple assets with application to option valuation, Mathematical and Computer Modeling, 48, No. 11-12, 1775-1786 (2008).

67.  Edward J. Allen, Derivation of stochastic partial differential equations, Stochastic Analysis and Applications, 26, 357-378 (2008).

68.  Edward J. Allen, Derivation of stochastic partial differential equations for size- and age-structured populations, Journal of Biological Dynamics, 3, No. 1, 73-86 (2009).

69.  Amy J. Ekanayake, Jo-Szu Tsai, Linda J. S. Allen, Loren M. Smith, James G. Surles, and Edward J. Allen, Estimating Watershed Area for Playas in the Southern High Plains, USA, Wetlands, 29, 387-395, 2009.

70.  E. J. Allen, C. Huff, Derivation of Stochastic Differential Equations for Sunspot Activity, Astronomy & Astrophysics, 516, Article Number A114, June-July 2010.

71.  E. J. Allen, X. Ji, A Stochastic Partial Differential Equation for Stock-Price Distributions, Proceedings of Neural, Parallel, and Scientific Computations, 4, 19-25, 2010.

72.  R. L. Paige, E. J. Allen, Closed-form Likelihoods for Stochastic Differential Equation Growth Models, Canadian Journal of Statistics, 38, 474-487 (2010).

73.  E. Dogan, E. J. Allen, Derivation Of Stochastic Partial Differential Equations For Reaction-Diffusion Processes, Stochastic Analysis and Applications, 29, 3, 424-443 (2011).

74.  E. J. Allen, Stochastic Difference Equations and a Stochastic Partial Differential Equation for Neutron Transport, Journal of Difference Equations and Applications, 18, 1267-1285 (2012).

75.  U. Bulut, E. J. Allen, Derivation of SPDEs for Correlated Random Walk Transport Models in One and Two Dimensions, Stochastic Analysis and Applications, 30, 553-567 (2012).

76.  Edward J. Allen, A Stochastic Analysis of Power Doubling Time for a Subcritical System, Stochastic Analysis and Applications, 31, 528-537 (2013).

77.  Edward J. Allen, John A. Burns, David S. Gilliam, Numerical Approximations of the Dynamical System Generated by Burgers' Equation with Neumann-Dirichlet Boundary Conditions, Mathematical Modelling and Numerical Analysis, 47, 1465-1492 (2013).

78.  U. Bulut, E. J. Allen, Derivation of SDEs for a Macroevolutionary Process, Discrete and Continuous Dynamical Systems - Series B, 18, 1777-1792 (2013).

79.  Edward Allen, Approximation of Triple Stochastic Integrals Through Region Subdivision, Communications in Applied Analysis, (Special Tribute Issue to Professor V. Lakshmikantham), 17, 355-366 (2013).

80.  Edward Allen, Derivation and computation of discrete delay and continuous delay SDEs in mathematical biology, Mathematical Biosciences and Engineering, 11, 403-425, doi:10.3934/mbe.2014.11.403, (2014)

81.  L. J. S. Allen and E. J. Allen, Deterministic and stochastic SIR epidemic models with power function transmission and recovery rates (book chapter, pages 1-15), In: AMS Contemporary Mathematics Series, Volume 618, Mathematics of Discrete and Continuous Dynamical Systems: In honor of the 70th birthday of Ronald E. Mickens, A. B. Gumel, Editor, (2014).

82.  M. Abukhaled, E. Allen, and N. Guessoum, Testing pulse density distribution for terrestrial gamma ray flashes, J. Geophys. Res. Space Physics, 119, doi:10.1002/2014JA020055, (2014).

83.  R. Leander, E. J. Allen, S. P. Garbett, D. R. Tyson, V. Quaranta, Derivation and experimental comparison of cell-division probability densities, Journal of Theoretical Biology, 359, 129135 (2014).

84.  Elife Dogan-Ciftci, Edward J. Allen, Derivation Of Several SDE Systems In One- And Two-Locus Population Genetics, Stochastic Analysis and Applications,32, 1-15 (2014).

Books

  1. Edward Allen, Modeling With Ito Stochastic Differential Equations, Springer, Dordrecht, The Netherlands (2007).
  2. Azmy S. Ackleh, Edward J. Allen, R. Baker Kearfott, Padmanabhan Seshaiyer, Classical and Modern Numerical Analysis: Theory, Methods and Practice, Chapman and Hall (2009).

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