
Submitted:
91. Q. Sheng and J. W. Haus, Effective semiimplicit shooting schemes for simulating the circularly
symmetric Townes profile, submitted.
90. Q. Sheng, S. Guha and L. Gonzalez, A compact domain splitting algorithm for the paraxial
Helmholtz equation in radially symmetric fields, submitted.

Appeared:
89. Q. Sheng, ADI, LOD and modern decomposition methods for certain multiphysics applications,
J. Algorithms Computat Tech, in press.
88. T. Zhu, A. Wang, G. Cleaver, K. Kirsten and Q. Sheng, Power spectra and spectral indices of
kinflation: highorder corrections, Phys. Review D, 90 (2014) 103517.
87. Q. Sheng and H. Sun, Exponential splitting for ndimensional
paraxial Helmholtz equation with high wavenumbers, Computers Math. Appl., 68 (2014), 13411354.
86. T. Zhu, A. Wang, G. Cleaver, K. Kirsten and Q. Sheng, Quantum effects on power spectra and spectral
indices with higherorder corrections, Phys. Review D, 90 (2014) 063503.
85. Q. Sheng, Adaptive decomposition methods for the solution of certain highly oscillatory optical
wave problems, ECT Proceedings, 9 (2014), 115132.
84. T. Zhu, A. Wang, G. Cleaver, K. Kirsten and Q. Sheng, Constructing analytically mode functions of
inflation with transPlanckian physics, Intern. J. Modern Phys. A, in press.
83. X. Liang, A. Khaliq and Q. Sheng, An efficient exponential time differencing
method for nonlinear Schrodinger equations, Appl. Math. Comptat., 235 (2014) 235252.
82. T. Zhu, A. Wang, G. Cleaver, K. Kirsten and Q. Sheng, Inationary cosmology with nonlinear
dispersion relations, Phys. Review D, 89 (2014) 043507.
81. M. Beauregard and Q. Sheng, A fully adaptive approximation for quenching type reactiondiffusion
equations over circular domains, Numer. Meth. PDEs, 30 (2014) 472489.
80. M. Beauregard and Q. Sheng, An adaptive splitting approach for the quenching solution of
reactiondiffusion equations over nonuniform grids, J. Comptat. Appl. Math., 241 (2013) 3044.
79. Q. Sheng and S. Guha, A compact splitting scheme approach on nonuniform grids,
Contemporary Mathematics, 586 (2013) 313321.
78. M. Beauregard and Q. Sheng, Explorations and expectations of equidistribution adaptations,
Adv. Appl. Math. Mech., 5 (2013), 407422.
77. M. Beauregard and Q. Sheng, Solving degenerate quenchingcombustion equations by an adaptive
splitting method on evolving grids, Computers & Structures, 122 (2013) 3343.
76. Q. Sheng and A. Khaliq, A revisit of the semiadaptive method for singular degenerate
reactiondiffusion equations, East Asia J. Appl. Math., 2 (2012), 185203.
75. M. Beauregard and Q. Sheng, A semiadaptive compact splitting method for the numerical
solution of 2dimensional quenching problems, Appl. Math. Comptat., 218 (2012), 1124011254.
74. Q. Sheng, S. Guha and L.P. Gonzalez, A short note on the asymptotic stability of certain
oscillationfree eikonal splitting schemes, Appl. Math. Lett., 25 (2012), 15391543.
73. Q. Sheng and H. Sun, On the stability of an oscillationfree ADI method for highly
oscillatory wave equations, Comm. Computat. Phys, 12 (2012), 12751292.
72. Q. Sheng, S. Guha and L.P. Gonzalez, Eikonal decomposition methods for fast computations
of beam propagations, Eng. Comptat., 29 (2011), 418.
71. Q. Sheng, S. Guha and L. Gonzalez, An exponential transformation based splitting method for
fast computations of highly oscillatory solutions, J. Comptat. Appl. Math., 235 (2011), 44524463.
70. Q. Sheng, J. W. Rogers and S. Guha, Effective stretching strategies for paraxial lightwave
propagation simulations, Computers & Structures, 87 (2009), 784792.
69. Q. Sheng and A. Wang, A study of the dynamic difference approximations on time
scales, International J. Difference Eqns, 4 (2009), 137153.
68. Q. Sheng, Adaptive decomposition finite difference methods for solving singular
problems, Frontiers of Math. in China, 4 (2009), 599626.
67. Q. Sheng, An effective semiimplicit method for circularly symmetric quenching
optical waves, Dynamic Sys. Appl., 18 (2009), 129142.
66. Q. Sheng, A. Khaliq and D. Voss, A special issue on financial derivatives, Inter. J.
Comput. Math., 86 (2009), 939939.
65. Q. Sheng, Recent trends in splitting, adaptive and hybrid numerical
methods for differential equations, Neural, Parallel and Sci. Comput. 16 (2008) 283301.
64. L. Gonzalez, S. Guha and Q. Sheng, Propagation of high intensity light in semiconductors,
Proc. Appl. Math. Mech., 7 (2008), 10412031041204.
63. L. Gonzalez, S. Guha, J. W. Rogers and Q. Sheng, An effective
zstretching method for paraxial light
beam propagation simulations, J. Computational Physics, 227
(2008), 72647278.
62. Q. Sheng, Hybrid approximations via second order crossed dynamic
derivatives with the $\diamondsuit_{\alpha}$ derivative, Nonlinear Anal.: Real World Appls., 9 (2008), 628640.
61. S. Guha, L. Gonzalez and Q. Sheng, Description of light focusing by a
spherical lens using diffraction integral
method, Proc. Appl. Math. Mech., 7 (2008), 10233011023302.
60. Q. Sheng, A movingmesh splitting scheme for 2dimensional
quenching problems, Proc. Appl. Math. Mech., 7 (2008), 10233031023304.
59. A. Khaliq and Q. Sheng, On monotonicity of an adaptive splitting scheme
for twodimensional singular reactiondiffusion equations, Inter. J. Computer Math., 84 (2007),
795806.
58. J. Ehrke, J. Henderson, C. Kunkel and Q. Sheng, Boundary data smoothness
for solutions of nonlocal boundary value problems for second order ordinary differential equations,
J. Math. Anal. Appl., 333 (2007), 191203.
57. Q. Sheng and J. W. Haus, On the $n$th mode numerical solutions of a second
order boundary value problem on semiinfinite domain, Communications on Applied Nonlinear Anal,
14 (2007), 121133.
56. Q. Sheng, Hybrid approximations via second order combined dynamic derivatives on time scales, Electronic
J. Qualitative Theory Diff. Eqns, 17 (2007), 113.
55. J. W. Rogers, Jr. and Q. Sheng, Notes on the diamond$\alpha$ dynamic derivative on time scales,
J. Math. Anal. Appl., 326 (2007), 228241.
54. Y. Lin, R. C. Hardie, Q. Sheng and M. Shao, Improved optimization of soft partition
weighted sum filters and their application to image restoration, Applied Optics, 45 (2006), 26972706.
53. J. M. Davis, J. Henderson, B. Karna, Q. Sheng and C. C. Tisdell, Existence of solutions for multipoint
boundary value problems for Nth order differential equations, J. Nonlinear Studies, 13 (2006) 1522.
52. Q. Sheng, M. Fadag, J. Henderson and J. M. Davis, An exploration of combined dynamic derivatives on time
scales and their applications, Nonlinear Anal.: Real World Appl., 7 (2006), 395413.
51. P. W. Eloe, S. Hilger and Q. Sheng, A qualitative analysis on
nonconstant graininess of the adaptive grid via time scales, Rocky
Mountain J. Math., 36 (2006), 115133.
50. C. Zhang, Q. Sheng and R. Ordonez, Notes on the convergence
and applications of dynamic surrogate optimization, Discrete and Continuous Dynamical Systems, S (2005), 947956.
49. Q. Sheng, A. Khaliq and D. Voss, Numerical simulation of twodimensional sineGordon solitons via a split cosine scheme, Math.
Computers Simulations, 68 (2005), 355373.
48. Q. Sheng, D. Voss and A. Khaliq, An adaptive splitting algorithm
for the sineGordon equation, Discrete and Continuous Dynamical Systems, S (2005), 792797.
47. Q. Sheng, A view of dynamic derivatives on time scales from approximations, J. Difference Eqn. Appl., 11 (2005) 6382.
46. Q. Sheng, Dynamic equations on time scales  a challenge to the traditional
computational concepts, Proc. CCCT'04, 5 (2004), 317322.
45. P. W. Eloe and Q. Sheng, Approximating crossed symmetric solutions of nonlinear dynamic equations via quasilinearization, Nonlinear Anal., 56 (2004), 253272.
44. H. Cheng, P. Lin, Q. Sheng and R. C. E. Tan, Solving degenerate reactiondiffusion
equations via variable step PeacemanRachford splitting, SIAM J. Scientific Computing,
25 (2003), 12731292.
43. Q. Sheng, R. D. Sudduth and K. Nichols, A simulation study of the injection
molded Syndiotactic Polystyrene crystallization process, J. Comput. Methods Sci. Eng.,
3 (2003), 233247.
42. P. W. Eloe and Q. Sheng, A continuation on cross symmetry of the solutions
of twopoint boundary value problems, Dynamic Sys. Appl.,
12 (2003), 99114.
41. P. W. Eloe, Q. Sheng and J. Henderson, Notes on crossed symmetry
solutions of boundary value problems on time scales, J. Difference Eqn. Appl.,
9 (2003), 2948.
40. R.D. Sudduth, Q. Sheng, R. Dugyala, J. Garber and K. Nichols,
Computer simulation of Syndiotactic Polystyrene crystallization during
injection molding, J. Injection Molding Tech., 6 (2002), 120142.
39. Q. Sheng and A. Q. M. Khaliq, Modified arclength adaptive algorithms for degenerate
reactiondiffusion equations, Applied Mathematics and Computations, 126 (2002), 279297.
38. Q. Sheng and H. Cheng, On monotone adaptive algorithms for solving singular
reactiondiffusion equations, Proc. Second International Conf. on Neural,
Parallel, and Scientific Computations, 2 (2002), 233236.
37. R. D. Sudduth, P. Yarala and Q. Sheng, Comparison of induction time and
crystallization rate for syndiotactic polystyrene, Polymer Engineering and Science.,
42 (2002), 694706.
36. Q. Sheng, A. Q. M. Khaliq and E. AlSaid, Solving the generalized nonlinear
Schrödinger equation via quartic spline approximations,
J. of Computational Physics, 166 (2001), 400417.
35. R. D. Sudduth, P. Yarala, Q. Sheng and K. Nichols, Measurement and simulation of
the crystallinity distribution in injection molded syndiotactic polystyrene,
Progress and Challenges  Third AFOSR International Conference, Greyden Press, Columbus,
OH, (2001), 637646.
34. Q. Sheng and A. Q. M. Khaliq, Linearly implicit adaptive schemes for singular
reactiondiffusion equations, Chapter 9, Adaptive Method of Lines (edited by William Schiesser,
Alain Vande Wouwer and Philippe Saucez), CRC Press, London and New York,
2001.
33. Q. Sheng and A. Q. M. Khaliq, Adaptive methods for convectiondiffusionreaction
equations of quenching type, Special Issue on Advances in Quenching, Dynamics of Continuous,
Discrete & Impulsive Sys., Series A, 8 (2001), 129148.
32. Q. Sheng, S. Duan and C. M. Hsiung, A simulation approach to crystallinity
gradients developed in the injection molding process of slowly crystallizing polymers,
J. Reinforced Plastics Composites, 19 (2000), 377395.
31. Q. Sheng and H. Cheng, An adaptive grid method for degenerate semilinear
quenching problems, Computers & Mathematics with Applications., 39 (2000), 5771.
30. A. Q. M. Khaliq, B. Abukhodair and Q. Sheng, A predictorcorrector scheme for the
sineGordon equation, Numerical Methods for Partial Differential Equations,
16 (2000), 133146.
29. Q. Sheng and H. Cheng, Notes on moving mesh computations for certain
degenerate combustion equations, Proc. Advanced Simulation Technologies
Conference, Washington D.C. (2000), 1924.
28. Q. Sheng, F. F. Farshad and S. Duan, A simulation of
crystallinity gradients in injection molded PPS polymers via parallel splitting,
Engineering Computations, 16 (1999) 892912.
27. Q. Sheng and C. M. Hsiung, On computer simulations of the crystallinity gradient
developed in injection molding processes of slowly crystallizing polymers, Proc.
6th International Conf. Composites Engineering (ICCE6), (1999),
767768.
26. Q. Sheng, A monotonically convergent adaptive method for nonlinear
combustion problems, Integral Methods in Science & Engineering, Research
Notes in Mathematics 418 (edited by B. Bertram, C. Constanda and A. Struthers), Chapman &
Hall/CRC, London and New York (1999), 310315.
25. Q. Sheng and A. Q. M. Khaliq, A compound adaptive approach to degenerate nonlinear
quenching problems, Numerical Methods for Partial Differential Equations, 15
(1999), 2947.
24. Q. Sheng and H. Cheng, A moving mesh approach to the numerical solution of
nonlinear degenerate quenching problems, Neural, Parallel Scientific Comput.
7, (1999), 343358.
23. Q. Sheng and C. M. Hsiung, Simulation of structure development during injection
molding of slowly crystallizing polymers, Proc. of 14th Annual PPS
Conf., Japan (1998), 1102.
22. Q. Sheng and R. P. Agarwal, Solutions of nonlinear partial integrodifferential
equations together with multipoint boundary values, J. Dynamic System &
Applications, 7 (1998), 1128.
21. C. M. Hsiung and Q. Sheng, A rectilinear flow model approach to the simulation
of the injection molding process, J. Reinforced Plastics Composites, 16 (1997),
12421251.
20. Q. Sheng and C. M. Hsiung, A splitting approach to the 3dimensional flow
simulation in the injection molding of semicrystalline polymers and polymer
composites, Proc. 4th International Conf. Composites Engineering (ICCE4)
(1997), 445.
19. Q. Sheng, On perturbed nonlinear difference equations together with multipoint
boundary conditions, Proc. International Conf. Dynamical Systems & Diff.
Equations, 5 (1997), 196208.
18. Q. Sheng and R. P. Agarwal, Solutions of npoint boundary value problems
associated with nonlinear summary difference equations, J. of Comp. Appl.
Math., 80 (1997), 4970.
17. R. P. Agarwal and Q. Sheng, Sharp integral inequalities in n independent
variables, Nonlinear Anal., 26 (1996), 179210.
16. Q. Sheng and T. Tang, Optimal convergence of an Euler and finite difference
method for nonlinear partial integrodifferential equations, Mathl. Comput.
Modelling, 21 (1995), 111.
15. R. P. Agarwal and Q. Sheng, Right focal point boundary value problems for
functionaldifferential equations, Boundary Value Problems for Functional
Differential Equations, (1995), 112, World Scientific.
14. Q. Sheng and R. P. Agarwal, Existence and uniqueness of the solutions of
nonlinear npoint boundary value problems, Nonlinear World, 2 (1995),
6986.
13. Q. Sheng, A note on asymptotic splitting and its applications, Mathl.
Comput. Modelling, 20 (1994), 4558.
12. Q. Sheng, Nonlinear variation of parameter methods for summary difference
equations in several independent variables, J. Appl. Math. Comp., 61 (1994),
3960.
11. Q. Sheng and R. P. Agarwal, Periodic solutions of higherorder difference
equations in two independent variables, Proc. Sym. Applied Math. (AMS), 48
(1994), 377381.
10. Q. Sheng and R. P. Agarwal, Monotone methods for higher order
partial difference equations, Comp. Math. Appl., 28 (1994), 291307.
9. Q. Sheng and R. P. Agarwal, Existence and uniqueness of periodic solutions for
higher order hyperbolic partial differential equations, J. Math. Anal. Appl.,
181 (1994), 392406.
8. Q. Sheng, Global error estimate for exponential splitting, IMA J. Numer.
Anal., 14 (1993), 2756.
7. R. P. Agarwal, Q. Sheng and P. Wong, On AbelGontscharoff boundary value problems,
Mathl. Comput. Modelling, 17 (1993), 3755.
6. Q. Sheng and R. P. Agarwal, On nonlinear variation of parameter methods for
summary difference equations, Dynamic Sys. Appl., 2 (1993), 227242.
5. Q. Sheng and R. P. Agarwal, Generalized maximum principle for higher order
ordinary differential equations, J. Math. Anal. Appl., 174 (1993), 476479.
4. Q. Sheng and P. Yap, Numerical solutions of systems of linear equations,
Math. Medley, 20 (1992), 1829.
3. Q. Sheng and R. P. Agarwal, Periodic solutions of higher order hyperbolic partial
differential equations, Panamer. Math. J., 2 (1992), 122.
2. Q. Sheng, Solving linear partial differential equations by exponential splitting,
IMA J. Numer. Anal., 9 (1989), 199212.
1. Q. Sheng, A uniformly convergent difference method for convectiondiffusion
singular perturbation problems in curved boundary regions, Applied
Math. & Mech., 7 (1986), 269278.

