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PUBLICATIONS: |
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A.Q.M. Khaliq and R.H.
Liu, New numerical scheme for pricing American Option
with regime- switching, International Journal of
Theoretical and Applied Finance, Vol. 12(3), 319-340,
2009.
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W. Liao and A. Q. M.
Khaliq, High order compact scheme for solving nonlinear
Black-Scholes equation with transaction cost,
International Journal of Computer Mathematics, Vol.
86(6), 1009-1023, 2009.
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A.Q.M. Khaliq, J. Martín-Vaquero,
B. A. Wade, M. Yousuf, Smoothing schemes for
reaction-diffusion systems with non smooth data, Journal
of Computational and Applied Mathematics, Vol.223,
374-386, 2009.
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A.Q.M. Khaliq, D.A. Voss,
K. Kazmi, Adaptive θ-methods for pricing American
options, Journal of Computational and Applied
Mathematics, Vol. 222(1), 210-227, 2008.
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A.Q.M. Khaliq, D. A.Voss
and G. E. Fasshauer, A parallel time stepping approach
using mesh free approximations for pricing options with
non-smooth payoffs, Journal of Risk, Vol.10(4), 135-142, 2008.
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A.Q.M. Khaliq, D.A. Voss, M. Yousuf, Pricing Exotic
Options with L-Stable Padé Schemes, Journal of Banking and
Finance, Vol. 31, 3438-3461, 2007.
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A.Q.M. Khaliq, B.A. Wade, M. Yousuf, J. Vigo-Aguiar, High
Order Smoothing Schemes for Inhomogeneous Parabolic Problems
with Applications in Option Pricing, Numerical Methods for
Partial Differential Equations, An International Journal, Vol.
23, 1249-1276, 2007.
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A Q M Khaliq, and Q
Sheng, On the monotonicity of an adaptive splitting
scheme for two-dimensional singular
reaction-diffusion equations, International Journal
of Computer Mathematics, Vol. 84(6), 795-806, 2007.
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B.A. Wade, A.Q.M.
Khaliq, M. Yousuf, J. Vigo-Aguiar, R. Deininger,
On smoothing of the Crank–Nicolson scheme and
higher order schemes for pricing barrier
options, Journal of Computational and Applied
Mathematics, Vol. 204, 144-158, 2007.
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A.Q.M. Khaliq,
D.A. Voss, and S.H.K. Kazmi, A Linearly
Implicit Predictor-Corrector Scheme for
Pricing American Options using a Penalty
Method Approach, Journal of Banking and
Finance, Vol. 30, 489-502, 2006.
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W. Liao,
J. Zhu, and A.Q.M. Khaliq, A Fourth
order compact algorithm for nonlinear
Reaction-diffusion equations with
Neumann boundary conditions,Numerical
Methods in Partial Differential
Equations, An International Journal,
Vol. 22(3), 600-616, 2006
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Q.
Sheng, A.Q.M.Khaliq, and D.A. Voss,
Numerical Simulation of
Two-Dimensional Sine-Gordon Solitons
via a Split Cosine Scheme,
Mathematics and Computers in
Simulation, Vol. 68(4) 355-373,
2005.
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B.
Wade, A.Q.M.Khaliq, and M.
Siddique, and M. Yousuf,
Smoothing with positivity
preserving Padé schemes for
parabolic problems, Numerical
Methods for Partial Differential
Equations, Vol. 21(3), 553-573,
2005.
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G. Fasshauer, A.Q.M. Khaliq,
and D.A. Voss, Using Mesh
free approximation for Multi
Asset American options,
(Special Issue on Mesh free
methods, Guest Editor, C.S.
Chen, University of Nevada,
Los Vegas), Journal of
Chinese Institute of
Engineers (JCIE) Vol. 27(4),
563-571, 2004.
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D.A.Voss, A.Q.M. Khaliq,
S.H.K. Kazmi, and H.He,
A Fourth Order L-Stable
method for the Black-Scholes
model with barrier
options, ( Eds. M.L.
Gavrilova, V. Kumar, and
C.J.K. Tan), Lecture
Notes in Computer
Science, Springer-Verlag
Heidelberg, Vol. 2669 ,
ISSN: 0302- 9743,
199-207, 2003.
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W. Liao, J.Zhu, and
A.Q.M.Khaliq, An
Efficient High order
Algorithm for
Solving System of
Reaction-Diffusion
Equations, Numerical
Methods for PDEs,
18(3), 340-354,
2002.
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Q. Sheng and
A.Q.M. Khaliq,
Modified
arc-length
adaptive
algorithms for
degenerate
reaction-diffusion
equations,
Applied
Mathematics and
Computation Vol.
126, 279-297,
2002
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A.Q.M.
Khaliq and
B.A.
Wade, On the
Smoothing of
Crank-Nicolson
Method for
Non
homogenous
Parabolic
Partial
Differential
Equations,
Journal of
Computational
Methods for
Sciences and
Engineering,
Vol. 1(1),
17-30, 2001
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Q. Sheng,
A. Q. M.
Khaliq,
and E.
Al-Said,
Solving
the
generalized
nonlinear
Schrödinger
equation
via
quartic
spline
approximations,
J. of
Computational
Physics,
Vol.
166(2),
400-417,
2001.
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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.,
Vol.
8,
129-148,
2001
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A.Q.M. Khaliq and Q.Sheng, Linearly Implicit Adaptive Schemes for Singular Reaction-Diffusion equations, in Adaptive Methods of Lines (eds. Wouwer; Alain Vande, Saucez; Phillippe, Schiesser; William E.) CRC Press, USA, ISBN/ISSN 158488231X, April 2001
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D.S. Daoud, A.Q.M.Khaliq, and B.A. Wade, A Non-overlapping Implicit Predictor-Corrector Scheme for Parabolic Equations, Proceedings of the International Conference on Parallel and Distributed Processing: Techniques and Applications (DPTA’2000), ed. H.R. Arabnia, Vol. I, pp.15-19, 2000, CSREA Press, Las Vegas, Nevada, USA.
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D.A. Voss and A.Q.M. Khaliq, Parallel Rosenbrock Methods for Chemical Systems, Computers & Chemistry, Vol. 25(1), 101-107, 2000.
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A.Q.M.Khaliq, B. Abukhoider, Q. Sheng, and M.S. Ismail, A Predictor-corrector Scheme for the sine-Gordon Equation, Numerical Methods for Partial Differential Equations: An International Journal, Vol. 16(2), 133-146, 2000
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D.A. Voss and A.Q.M. Khaliq, A Linearly Implicit Predictor-Corrector Method for the Reaction-Diffusion Equations, Computers & Mathematics with Applications, Vol. 38(11-12), 207-216, 1999
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Q. Sheng and A.Q.M. Khaliq, A Compound Adaptive Approach to Degenerate Nonlinear Quenching Problems, Numerical methods for Partial Differential Equations: An International Journal, Vol. 15, 29-47,1999.
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D.A.Voss and A.Q.M. Khaliq, Time-Stepping Algorithm for Parabolic PDEs Based on Rational Approximants with Distinct Real Poles, Advances in Computational Mathematics, Vol. 7, 353-363,1997.
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A.Q.M. Khaliq and D.A.Voss, A Predictor Corrector Scheme for Reaction Diffusion Equations, ZAMM, Vol. 76(S1), 577-578, 1996.
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D.A.Voss and A.Q.M. Khaliq, Parallel LOD Methods for Multidimensional PDEs”,Computers & Math. with Applications, Vol. 30(10), 25-35, 1995
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A. Q. M. Khaliq, E. H. Twizell, and D. A. Voss “On Parallel Algorithms for Semidiscretized Parabolic Partial Differential Equations Based on Subdiagonal Pade Approximations”, Numerical Methods for Partial Differential Equations, Vol. 9(2), 107-116, 1993.
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A. Q. M. Khaliq and D. A. Voss, A parallel Fourth Order Method for Second Order Hyperbolic PDEs, in R. F. Sincovec (ed), Proceedings of the sixth SIAM Conference on “Parallel Processing for Scientific Computing’, 586-589, 1993.
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E.H.Twizell, A.Q.M. Khaliq and D.A.Voss, Sequential and Parallel Algorithms for Second Order Initial Value Problems, in CONTRIBUTIONS IN NUMERICAL MATHEMATICS (R.P. Agarwal, Ed), [World Scientific Series in Applicable Analysis, Vol. 2], World Scientific, Singapore, 399-412, 1993.
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D.A.Voss and A.Q.M. Khaliq, A Parallel Splitting Methods For Second Order Multidimensional Hyperbolic Partial Differential Equations, in R. Vichnevtskey, D. Knight and G. Ritcher (Eds.), “Advances in Computer Methods for Partial Differential Equations” VII, 411-417, 1992
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E.H. Twizell, S.A. Matar, D.A. Voss and A.Q.M. Khaliq, Explicit Numerical Methods With Enhanced Stability Properties For First -Order Autonomous Initial-Value Problems, International J of Eng. Science, Vol. 30(3), 379-392, 1992
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A.Q.M. Khaliq, E.H. Twizell, and A.Y. Al-Hawaj, Dynamic Analysis of Cantilever Beam by Finite Element Method, In MAFLAP 90 (J.R. Whiteman, ed), Academic Press, 471-478, 1991
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M. Bashir, A.Q.M. Khaliq, A.Y. Al-Hawaj and E.H. Twizell, An Explicit Difference Model for Tidal Flows in the Arabian Gulf, in W.L. Hogarth and B.J. Noye (eds.), Proceedings of the International Conference on “Computational Techniques and Applications”, Australia: CTAC-89, Hemisphere Publishing Co., 295-302, 1990
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A.Q.M. Khaliq and E.H. Twizell, Global Extrapolation of Numerical Methods for Initial Value Problems, Applied Math. & Computation, Vol. 31,148-169, 1989.
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D.A.Voss and A.Q.M. Khaliq, A Sixth Order Predictor-Corrector Methods for Periodic Initial Value Problems, Applied Mathematics Letters, Vol. 2(1), 65-68, 1989.
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E.H. Twizell and A.Q.M. Khaliq, A Family of Predictor-Corrector Methods for Second Order Hyperbolic Equations, Communications in Applied Numerical Methods, Vol. 5,47-51, 1989.
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A.Q.M. Khaliq and E.H. Twizell, Global Extrapolation on Three and four Grids for Special Initial Value Problems, Applied Mathematics Letter, Vol. 2(1), 35-37,1989.
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A.Q.M. Khaliq, A Predictor-Corrector Scheme for Fourth Order Parabolic Partial Differential Equations, Computer and Mathematics with Applications, Vol. 17(12), 1563-1566, 1989.
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A.Q.M. Khaliq and E.H. Twizell,The Effect of Global Extrapolation on the Phase-Lag of Symmetric Methods for Solving Periodic Initial Value Problems, International Journal of Computer Mathematics, Vol. 28, 161-169, 1989.
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F. S. H. Al-Sadah, A. Q. M. Khaliq and M. Bashir, Finite difference Analysis for Navier-Stokes and Energy Equations of Couette-Poiseuille Flow, in J. Noye and C. Flethcher (eds.), CTAC-87, North Holland, 71-81, 1988.
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E. H. Twizell and A. Q. M. Khaliq, Global extrapolation Methods for the Fourth Order Parabolic Partial Differential Equation, Arabian Gulf Journal of Scientific Research, Vol. A6 (1), 1-15, 1988.
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A. Q. M. Khaliq and E. H. Twizell, Methods with 0(h4) and 0(h6) phase lags for the periodic initial value problems, International Journal of Computer Mathematics, Vol. 25, 49-54, 1988.
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A. Q. M. Khaliq and E. H. Twizell, A family of second order methods for variable coefficient fourth order parabolic partial differential equations, International Journal of Computer Mathematics, Vol. 23, 63-76, 1987
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A. Q. M. Khaliq and E. H. Twizell, Lo-stable splitting methods for the simple heat equation in two space dimensions with homogenous boundary conditions, SIAM Journal on Numerical Analysis, Vol. 23 (3), 473-484, 1986.
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A. Q. M. Khaliq and E. H. Twizell, A Family of Numerical Methods for Diffusion and reaction-diffusion equations, Numerical Methods for partial differential equations, Vol. 2, 31-45, 1986.
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E. H. Twizell and A. Q. M. Khaliq, Lo-stable methods for constant coefficient parabolic equations’ in Haqmoui (ed), proceedings of the conference on Mathematical analysis and its Applications, Univ. of Kuwait, 349-358, 1985.
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E. H. Twizell and A. Q. M. Khaliq, Reaction-diffusion equations in mathematical biology, in J. C. Lion and B. N. Feinberg (eds), Proceedings of the Seventh Annual Conference of the IEEE/ENG. in Med. and Biol/ Soc; 1292-1295, IEEE, New York, 1985.
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A. Q. M. Khaliq and A. Y. Al-Hawaj, A third order finite difference methods for two dimensional parabolic equations, in Hamoui (ed.), proceedings of the conference on Mathematical analysis and its Applications, Univ. of Kuwait, 281-288, 1985.
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A. Q. M. Khaliq and E. H. Twizell, Stability regions for one step multidirective methods in PECE mode with applications to stiff system, International Journal of Computer Mathematics, Vol. 17, 323-338, 1985.
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E. H. Twizell and A. Q. M. Khaliq, Multiderivative methods for periodic initial value problems, SIAM Journal on Numerical Analysis, Vol. 21 (1), 111-122, 1984
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A. Q. M. Khaliq and E. H. Twizell, Backward difference replacements of the space derivative in first order hyperbolic equations, Computer Methods in Applied Mechanics and Engineering, Vol. 43 (1), 45-56, 1984.
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E. H. Twizell and A. Q. M. Khaliq, A difference scheme with high accuracy in time for fourth order parabolic equations, Computer Methods in Applied Mechanics and Engineering’, Vol. 41, 91 –104, 1983.
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A. Q. M. Khaliq and E. H.Twizell, The extrapolation of stable finite difference schemes for first order hyperbolic equations, International Journal of Computer Mathematics, Vol. 11, 155-167, 1982.
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E. H. Twizell and A. Q. M. Khaliq, One-step Multiderivative methods for first order ordinary differential equations, BIT, Vol. 21(4), 518-527, 1981 |
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