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 Submitted: 88.  Q. Sheng and H. Sun, Exponential splitting for n-dimensional paraxial Helmholtz equation with high wavenumbers, submitted. 87.  Q. Sheng and J. W. Haus, Effective semi-implicit shooting schemes for simulating the circularly symmetric Townes profile, submitted. 86.  Q. Sheng, S. Guha and L. Gonzalez, A compact domain splitting algorithm for the paraxial Helmholtz equation in radially symmetric fields, submitted. 85.  T. Zhu, A. Wang, G. Cleaver, K. Kirsten and Q. Sheng, Constructing analytically mode functions of inflation with trans-Planckian physics, submitted. 84.  Q. Sheng, ADI, LOD and modern decomposition methods for certain multiphysics applications, submitted.
 Appeared: 83.  X. Liang, A. Khaliq and Q. Sheng, An efficient exponential time differencing method for nonlinear Schrodinger equations, Appl. Math. Comptat., in press. 82.  T. Zhu, A. Wang, G. Cleaver, K. Kirsten and Q. Sheng, Inationary cosmology with nonlinear dispersion relations, Phys. Review D, in press. 81.  M. Beauregard and Q. Sheng, A fully adaptive approximation for quenching type reaction-diffusion equations over circular domains, Numer. Meth. PDEs, in press. 80.  M. Beauregard and Q. Sheng, An adaptive splitting approach for the quenching solution of reaction-diffusion equations over nonuniform grids, J. Comptat. Appl. Math., 241 (2013) 30-44. 79.  Q. Sheng and S. Guha, A compact splitting scheme approach on nonuniform grids, Contemporary Mathematics, 586 (2013) 313-321. 78.  M. Beauregard and Q. Sheng, Explorations and expectations of equidistribution adaptations, Adv. Appl. Math. Mech., 5 (2013), 407-422. 77.  M. Beauregard and Q. Sheng, Solving degenerate quenching-combustion equations by an adaptive splitting method on evolving grids, Computers & Structures, 122 (2013) 33-43. 76.  Q. Sheng and A. Khaliq, A revisit of the semi-adaptive method for singular degenerate reaction-diffusion equations, East Asia J. Appl. Math., 2 (2012), 185-203. 75.  M. Beauregard and Q. Sheng, A semi-adaptive compact splitting method for the numerical solution of 2-dimensional quenching problems, Appl. Math. Comptat., 218 (2012), 11240-11254. 74.  Q. Sheng, S. Guha and L.P. Gonzalez, A short note on the asymptotic stability of certain oscillation-free eikonal splitting schemes, Appl. Math. Lett., 25 (2012), 1539-1543. 73.  Q. Sheng and H. Sun, On the stability of an oscillation-free ADI method for highly oscillatory wave equations, Comm. Computat. Phys, 12 (2012), 1275-1292. 72.  Q. Sheng, S. Guha and L.P. Gonzalez, Eikonal decomposition methods for fast computations of beam propagations, Eng. Comptat., 29 (2011), 4-18. 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), 4452-4463. 70.  Q. Sheng, J. W. Rogers and S. Guha, Effective stretching strategies for paraxial lightwave propagation simulations, Computers & Structures, 87 (2009), 784-792. 69.  Q. Sheng and A. Wang, A study of the dynamic difference approximations on time scales, International J. Difference Eqns, 4 (2009), 137-153. 68.  Q. Sheng, Adaptive decomposition finite difference methods for solving singular problems, Frontiers of Math. in China, 4 (2009), 599-626. 67.  Q. Sheng, An effective semi-implicit method for circularly symmetric quenching optical waves, Dynamic Sys. Appl., 18 (2009), 129-142. 66.  Q. Sheng, A. Khaliq and D. Voss, A special issue on financial derivatives, Inter. J. Comput. Math., 86 (2009), 939-939. 65.  Q. Sheng, Recent trends in splitting, adaptive and hybrid numerical methods for differential equations, Neural, Parallel and Sci. Comput. 16 (2008) 283-301. 64.  L. Gonzalez, S. Guha and Q. Sheng, Propagation of high intensity light in semiconductors, Proc. Appl. Math. Mech., 7 (2008), 1041203-1041204. 63.  L. Gonzalez, S. Guha, J. W. Rogers and Q. Sheng, An effective z-stretching method for paraxial light beam propagation simulations, J. Computational Physics, 227 (2008), 7264-7278. 62.  Q. Sheng, Hybrid approximations via second order crossed dynamic derivatives with the $\diamondsuit_{\alpha}$ derivative, Nonlinear Anal.: Real World Appls., 9 (2008), 628-640. 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), 1023301-1023302. 60.  Q. Sheng, A moving-mesh splitting scheme for 2-dimensional quenching problems, Proc. Appl. Math. Mech., 7 (2008), 1023303-1023304. 59.  A. Khaliq and Q. Sheng, On monotonicity of an adaptive splitting scheme for two-dimensional singular reaction-diffusion equations, Inter. J. Computer Math., 84 (2007), 795-806. 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), 191-203. 57.  Q. Sheng and J. W. Haus, On the $n$-th mode numerical solutions of a second order boundary value problem on semi-infinite domain, Communications on Applied Nonlinear Anal, 14 (2007), 121-133. 56.  Q. Sheng, Hybrid approximations via second order combined dynamic derivatives on time scales, Electronic J. Qualitative Theory Diff. Eqns, 17 (2007), 1-13. 55.  J. W. Rogers, Jr. and Q. Sheng, Notes on the diamond-$\alpha$ dynamic derivative on time scales, J. Math. Anal. Appl., 326 (2007), 228-241. 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), 2697-2706. 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) 15-22. 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), 395-413. 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), 115-133. 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), 947-956. 49.  Q. Sheng, A. Khaliq and D. Voss, Numerical simulation of two-dimensional sine-Gordon solitons via a split cosine scheme, Math. Computers Simulations, 68 (2005), 355-373. 48.  Q. Sheng, D. Voss and A. Khaliq, An adaptive splitting algorithm for the sine-Gordon equation, Discrete and Continuous Dynamical Systems, S (2005), 792-797. 47.  Q. Sheng, A view of dynamic derivatives on time scales from approximations, J. Difference Eqn. Appl., 11 (2005) 63-82. 46.  Q. Sheng, Dynamic equations on time scales - a challenge to the traditional computational concepts, Proc. CCCT'04, 5 (2004), 317-322. 45.  P. W. Eloe and Q. Sheng, Approximating crossed symmetric solutions of nonlinear dynamic equations via quasilinearization, Nonlinear Anal., 56 (2004), 253-272. 44.  H. Cheng, P. Lin, Q. Sheng and R. C. E. Tan, Solving degenerate reaction-diffusion equations via variable step Peaceman-Rachford splitting, SIAM J. Scientific Computing, 25 (2003), 1273-1292. 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), 233-247. 42.  P. W. Eloe and Q. Sheng, A continuation on cross symmetry of the solutions of two-point boundary value problems, Dynamic Sys. Appl., 12 (2003), 99-114. 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), 29-48. 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), 120-142. 39.  Q. Sheng and A. Q. M. Khaliq, Modified arc-length adaptive algorithms for degenerate reaction-diffusion equations, Applied Mathematics and Computations, 126 (2002), 279-297. 38.  Q. Sheng and H. Cheng, On monotone adaptive algorithms for solving singular reaction-diffusion equations, Proc. Second International Conf. on Neural, Parallel, and Scientific Computations, 2 (2002), 233-236. 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), 694-706. 36.  Q. Sheng, A. Q. M. Khaliq and E. Al-Said, Solving the generalized nonlinear Schrödinger equation via quartic spline approximations, J. of Computational Physics, 166 (2001), 400-417. 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), 637-646. 34.  Q. Sheng and A. Q. M. Khaliq, Linearly implicit adaptive schemes for singular reaction-diffusion 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 convection-diffusion-reaction equations of quenching type, Special Issue on Advances in Quenching, Dynamics of Continuous, Discrete & Impulsive Sys., Series A, 8 (2001), 129-148. 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), 377-395. 31.  Q. Sheng and H. Cheng, An adaptive grid method for degenerate semilinear quenching problems, Computers & Mathematics with Applications., 39 (2000), 57-71. 30.  A. Q. M. Khaliq, B. Abukhodair and Q. Sheng, A predictor-corrector scheme for the sine-Gordon equation, Numerical Methods for Partial Differential Equations, 16 (2000), 133-146. 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), 19-24. 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) 892-912. 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 (ICCE-6), (1999), 767-768. 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), 310-315. 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), 29-47. 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), 343-358. 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 integro-differential equations together with multi-point boundary values, J. Dynamic System & Applications, 7 (1998), 11-28. 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), 1242-1251. 20.  Q. Sheng and C. M. Hsiung, A splitting approach to the 3-dimensional flow simulation in the injection molding of semi-crystalline polymers and polymer composites, Proc. 4th International Conf. Composites Engineering (ICCE-4) (1997), 445. 19.  Q. Sheng, On perturbed nonlinear difference equations together with multi-point boundary conditions, Proc. International Conf. Dynamical Systems & Diff. Equations, 5 (1997), 196-208. 18.  Q. Sheng and R. P. Agarwal, Solutions of n-point boundary value problems associated with nonlinear summary difference equations, J. of Comp. Appl. Math., 80 (1997), 49-70. 17.  R. P. Agarwal and Q. Sheng, Sharp integral inequalities in n independent variables, Nonlinear Anal., 26 (1996), 179-210. 16.  Q. Sheng and T. Tang, Optimal convergence of an Euler and finite difference method for nonlinear partial integro-differential equations, Mathl. Comput. Modelling, 21 (1995), 1-11. 15.  R. P. Agarwal and Q. Sheng, Right focal point boundary value problems for functional-differential equations, Boundary Value Problems for Functional Differential Equations, (1995), 1-12, World Scientific. 14.  Q. Sheng and R. P. Agarwal, Existence and uniqueness of the solutions of nonlinear n-point boundary value problems, Nonlinear World, 2 (1995), 69-86. 13.  Q. Sheng, A note on asymptotic splitting and its applications, Mathl. Comput. Modelling, 20 (1994), 45-58. 12.  Q. Sheng, Nonlinear variation of parameter methods for summary difference equations in several independent variables, J. Appl. Math. Comp., 61 (1994), 39-60. 11.  Q. Sheng and R. P. Agarwal, Periodic solutions of higher-order difference equations in two independent variables, Proc. Sym. Applied Math. (AMS), 48 (1994), 377-381. 10.  Q. Sheng and R. P. Agarwal, Monotone methods for higher order partial difference equations, Comp. Math. Appl., 28 (1994), 291-307. 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), 392-406. 8.  Q. Sheng, Global error estimate for exponential splitting, IMA J. Numer. Anal., 14 (1993), 27-56. 7.  R. P. Agarwal, Q. Sheng and P. Wong, On Abel-Gontscharoff boundary value problems, Mathl. Comput. Modelling, 17 (1993), 37-55. 6.  Q. Sheng and R. P. Agarwal, On nonlinear variation of parameter methods for summary difference equations, Dynamic Sys. Appl., 2 (1993), 227-242. 5.  Q. Sheng and R. P. Agarwal, Generalized maximum principle for higher order ordinary differential equations, J. Math. Anal. Appl., 174 (1993), 476-479. 4.  Q. Sheng and P. Yap, Numerical solutions of systems of linear equations, Math. Medley, 20 (1992), 18-29. 3.  Q. Sheng and R. P. Agarwal, Periodic solutions of higher order hyperbolic partial differential equations, Panamer. Math. J., 2 (1992), 1-22. 2.  Q. Sheng, Solving linear partial differential equations by exponential splitting, IMA J. Numer. Anal., 9 (1989), 199-212. 1.  Q. Sheng, A uniformly convergent difference method for convection-diffusion singular perturbation problems in curved boundary regions, Applied Math. & Mech., 7 (1986), 269-278.

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