Dr. Edward J.
Allen
Professor Emeritus


Welcome to the home page of Edward
J. Allen at Texas Tech University
, Department of Mathematics and
Statistics.
Numerical analysis, Stochastic differential equations,
Mathematical modeling
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, 461462 (1975). (See also
ORNLTM4814.)
3. E. J. Allen, CACA2: A
Revised Version of CACA  A Heavy Isotope and Fission Product
Concentration Calculational Code for
Experimental Irradiation Capsules, ORNL/TM5266, (February, 1976). (See also
RSIC Code Package CCC302, 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 InCore
Nuclear Heating Rates , Transactions of the
American Nuclear Society, 26, 605606 (1977).
5. E. J. Allen, J. E. Rushton,
M. M. Chiles, and J. D. Jenkins, Evaluation of a Nondestructive Assay Technique
for OnLine Assay of Fuel Rods in an HTGR Fuel Refabrication
Plant , Transactions of the American Nuclear Society, 33 , 441442
(1979). (See also ORNLTM6960.)
6. E. J. Allen and S. R. McNeany, Nondestructive Fissile Isotopic Measurement
Technique for Uranium233  Uranium235 Fuels Using Prompt and Delayed Fission
Neutron Counting , Nuclear Technology, 47, 363377 (1980).
7. E. J. Allen, An Application
of Global Approximations in the Finite Element Method ,
International Journal for Numerical Methods in Engineering, 21,
17491758 (1985).
8. E. J. Allen, Continued
Radicals, , The Mathematical Gazette, 69,
261263 (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,
449478 (1986).
10. E. J. Allen, On the Error in Pade Approximation , SIAM Review
(problem section), 30, 319320 (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, 229274
(1988).
12. E. J. Allen, Application of
Richardson Extrapolation to Numerical Solution of the Neutron Transport Equation , Nuclear Science and Engineering, 99,
123132 (1988).
13. E. J. Allen, H. D. Victory,
Jr., and K. Ganguly, On the Convergence of
FiniteDifferenced Multigroup, DiscreteOrdinates
Methods for Anisotropically Scattering Slab Media , SIAM
Journal on Numerical Analysis, 26, 88106 (1989).
14. E. J. Allen, Richardson
Extrapolation of the StepCharacteristic Method in Rectangular Geometry , Annals of Nuclear Energy, 16, 159172 (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, 137145 (1990).
16. H. D. Victory, Jr. and E. J.
Allen, The Convergence Theory of ParticleinCell Methods for VlasovPoisson Systems , SIAM
Journal on Numerical Analysis, 28, 12071241 (1991).
17. K. Ganguly,
E. J. Allen, and H. D. Victory, Jr., A New Approach to Neutron Transport , Transport Theory and Statistical Physics, 20,
329 (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, 278288 (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, 79,11231135 (1991).
20. E. J. Allen, J. M. Harris,
and L. J. S. Allen, PersistenceTime Models For Use In Viability Analyses of
Vanishing Species , Journal of Theoretical Biology, 155, 3353 (1992).
21. K. Ganguly,
G. Tucker, E. J. Allen, H. D. Victory, Jr., SNCONV Computer Code Abstract , Nuclear
Science and Engineering, 110, 205206 (1992).
22. F. A. Mohamed, E. J. Allen,
and K. Rainwater, Well Response Tests: III. The Inverse Problem, Inverse
Problems, 9, 483493 (1993).
23. E. J. Allen, Requirements for
LongTerm 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, 239250 (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, 233234
(1993).
26. E. J. Allen and H. D.
Victory, Jr., A Computational Investigation of the Random Particle Method for
Numerical Solution of the Kinetic VlasovPoissonFokkerPlanck
Equations , Physica A, 209, 318346
(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, 131140 (1994).
28. E. J. Allen, International
Harvesters, Texas Parks and Wildlife, 3637 (July 1995).
29. E. J. Allen and C. J. Nunn,
Difference Methods for Numerical Solution of Stochastic TwoPoint
BoundaryValue 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, 455481 (1996).
31. E. J. Allen, Harvester Ants:
Specialists in Plant Seeds, New Mexico Wildlife, 2223 (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, 815834
(1996).
33. M. I. Abukhaled
and E. J. Allen, A Class of SecondOrder RungeKutta
Methods for Numerical Solution of Stochastic Differential Equations
, Stochastic Analysis and Applications, 16, 977991 (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, 5366 (1998).
35. E. J. Allen, S. J. Novosel, Z. Zhang, Finite Element and Difference
Approximation of Some Linear Stochastic Partial Differential Equations , Stochastics, 64, 117142 (1998).
36. W. D. Sharp and E. J. Allen,
Numerical Solution of First Passage Time Problems Using An Approximate
ChapmanKolmogorov Relation , Probabilistic Engineering Mechanics, 13,
233241 (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, 488503 (1999).
38. E. J. Allen, Stochastic
differential equations and persistence time of two interacting populations , Dynamics of Continuous, Discrete, and
Impulsive Systems, 5, 271281 (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, 1530 (1999).
40. W. D. Sharp and E. J. Allen,
Stochastic neutron transport equations for rod and plane geometries
, Annals of Nuclear Energy, 27, 99116 (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, 167181 (2000).
42. E. J. Allen, Requirements for
LongTerm Persistence of the Texas Horned Lizard, Phrynosomatics,
(Special 10th Anniversary Issue), 1011 (December 2000).
43. E. J. Allen, Random selection
of 3digit numbers , Mathematical Spectrum, 33,
810 (2000/2001).
44. M. Chowdhury and E. J. Allen,
A stochastic continuoustime agestructured population model, Nonlinear
Analysis, 47, 14771488 (2001).
45. Marwan Abukhaled
and Edward J. Allen, Expectation stability of secondorder weak numerical
methods for stochastic differential equations, Stochastic Analysis and
Applications, 20, 693707 (2002).
46. E. J. Allen and R. M. Berry,
The inverse power method for calculation of multiplication factors, Annals
of Nuclear Energy, 29, 929935 (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,
11651195 (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, 7174 (2002).
49. E. J. Allen and C. M.
Thompson, A stochastic differential equation model for chargedparticle energy
straggling, Dynamics of Continuous, Discrete and Impulsive Systems Series B:
Applications and Algorithms 10,1927 (2003).
50. Armando Arciniega
and Edward Allen, Rounding error in numerical solution of stochastic
differential equations, Stochastic Analysis and Applications, 21,
281300 (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, 457486 (2003).
52. E. J. Allen and H. D.
Victory, Jr., Modelling and simulation of a schistosomiasis
infection with biological control, Acta Tropica, 87, 251267 (2003).
53. Armando Arciniega
and Edward Allen, Extrapolation of difference methods in option valuation, Applied
Mathematics and Computation, 153, 165186 (2004).
54. Armando Arciniega
and Edward Allen, Shooting methods for numerical solution of stochastic
boundaryvalue problems, Stochastic Analysis and Applications, 22, 120
(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, 439449 (2003).
56. J. S. Severino,
E. J. Allen, H. D. Victory, Jr., Acceleration of quasiMonte Carlo
approximations with applications in mathematical finance, Applied
Mathematics and Computation, 148, 173187 (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, 10391051
(2004).
58. Edward J. Allen,
Jumpdiffusion model for the global spread of an amphibian disease, International
Journal of Numerical Analysis and Modeling, 1, 173187 (2004).
59. Edward J. Allen, Linda J. S.
Allen, Henri Schurz, A comparison of persistencetime estimation for discrete
and continuous stochastic population models that include demographic and
environmental variability, Mathematical Biosciences, 196, 1438 (2005).
60. J. G. Hayes and E. J. Allen,
Stochastic pointkinetics equations in nuclear reactor dynamics, Annals of
Nuclear Energy, 32, 572587 (2005).
61. Rachel Koskodan
and Edward Allen, Extrapolation of the stochastic theta numerical method for
stochastic differential equations, Stochastic Analysis and Applications, 24,
475487 (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. CastilloChavez, 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, 116 (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, 245250 (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, 181192 (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, 274297 (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. 1112, 17751786 (2008).
67. Edward J. Allen, Derivation
of stochastic partial differential equations, Stochastic Analysis and
Applications, 26, 357378 (2008).
68. Edward J. Allen, Derivation
of stochastic partial differential equations for size and agestructured
populations, Journal of Biological Dynamics, 3, No. 1, 7386 (2009).
69. Amy J. Ekanayake,
JoSzu 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, 387395,
2009.
70. E. J. Allen, C. Huff,
Derivation of Stochastic Differential Equations for Sunspot Activity, Astronomy
& Astrophysics, 516, Article Number A114, JuneJuly 2010.
71. E. J. Allen, X. Ji, A Stochastic Partial Differential Equation for
StockPrice Distributions, Proceedings of Neural, Parallel, and Scientific
Computations, 4, 1925, 2010.
72. R. L. Paige, E. J. Allen,
Closedform Likelihoods for Stochastic Differential Equation Growth Models, Canadian
Journal of Statistics, 38, 474487 (2010).
73. E. Dogan,
E. J. Allen, Derivation Of Stochastic Partial Differential Equations For
ReactionDiffusion Processes, Stochastic Analysis and Applications, 29,
3, 424443 (2011).
74. E. J. Allen, Stochastic
Difference Equations and a Stochastic Partial Differential Equation for Neutron
Transport, Journal of Difference Equations and Applications, 18,
12671285 (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,
553567 (2012).
76. Edward J. Allen, A Stochastic
Analysis of Power Doubling Time for a Subcritical System, Stochastic
Analysis and Applications, 31, 528537 (2013).
77. Edward J. Allen, John A.
Burns, David S. Gilliam, Numerical Approximations of the Dynamical System
Generated by Burgers' Equation with NeumannDirichlet
Boundary Conditions, Mathematical Modelling and Numerical Analysis, 47,
14651492 (2013).
78. U. Bulut,
E. J. Allen, Derivation of SDEs for a Macroevolutionary
Process, Discrete and Continuous Dynamical Systems  Series B, 18,
17771792 (2013).
79.
Edward
Allen, Approximation of Triple Stochastic Integrals Through
Region Subdivision, Communications in Applied Analysis, (Special Tribute Issue
to Professor V. Lakshmikantham), 17, 355366 (2013).
80. Edward Allen, Derivation and
computation of discrete delay and continuous delay SDEs in mathematical
biology, Mathematical Biosciences and Engineering, 11, 403425, 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 115), 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 celldivision probability densities, Journal of Theoretical Biology, 359, 129–135
(2014).
84. Elife DoganCiftci, Edward
J. Allen, Derivation Of Several SDE Systems In One And TwoLocus Population
Genetics, Stochastic Analysis and Applications,32, 115 (2014).
Books