# Publications

## Guest Editor of Special Issues

- Guest Editor (with K.M. Furati,C. Li, M. Zayernouri) Special Issue, Advances on Computational
Fractional PDEs, International Journal of Computer Mathematics, Vol
**. 95**(6-7), 2018. - Guest Editor (with Q. Sheng and J. Ku) Special issue, Recent Advances on the Numerical
Methods for Systems of PDEs, Journal of Computational and Applied Mathematics, Vol.
**299**, 2016. - Guest Editor for the Special Issue, Financial Derivatives, International Journal of
Computer Mathematics, Vol.
**86**(6), 2009. - Guest Editor (with David Voss) for the Special Issue, Numerical PDE Methods in Finance,
Journal of Computational and Applied Mathematics,
**222**(1), 2008. - Guest Editor (with Q. Sheng) for the special Issue, Splitting Methods for Differential
Equations, International Journal of Computer Mathematics,
**84**(6), June 2007 - Co-Editor (with G. Fasshauer, J. Vigo Aguiar, and B. A. Wade), Proceedings of the International Conference on Computational and Mathematical Methods in Science and Engineering, Illinois Institute of Technology, Chicago, USA, 20-23 June, 2007
- Guest Technical Editor for the Theme Issue, Numerical Methods for Differential Equations
and Applications, Arabian Journal for Science and Engineering, John Wiley,
**22**(2C), Dec. 1997.

## Papers Published in Refereed Journals

- S. Hansun, F.P. Putri, A.Q.M. Khaliq, H. Hugeng, on searching the best mode for forex forecasting: bidirectional long short-term memory default mode is not enough, IAES International Journal of Artificial Intelligence, 11(4), 1596-1606. 2022.
- Seng Hansun, Arya Wickson and Abdul Q. M. Khaliq, Multivariate cryptocurrency prediction: comparative analysis of three recurrent neural networks approaches, Journal of Big Data 9:50,2022, https://doi.org/10.1186/s40537-022-00601-7
- Lin Feng, Ziren Chen, Harold A. Lay, Jr., Khaled Furati, and Abdul Khaliq, Data driven time-varying SEIR-LSTM/GRU algorithms to track the spread of COVID-19, Mathematical Bio Sciences and Engineering, 19(9), 8935–8962, 2022.
- Ibrahim O. Sarumi, Khaled M. Furati, Kassem Mustapha, Abdul Q. M. Khaliq, Efficient high-order exponential time differencing methods for nonlinear fractional differential models, Numerical Algorithms, 2022, https://doi.org/10.1007/s11075-022-01339-2.
- Ziren Chen, Lin Feng, Harold A. Lay Jr., Khaled Furati, Abdul Khaliq, SEIR model with unreported infected population and dynamic parameters for the spread of COVID-19, Mathematics and Computers in Simulation, 198, 31-46, 2022.
- T. A. Biala, Y.O. Afolabi, A.Q.M. Khaliq, how efficient is contact tracing in mitigating the spread of COVID-19? A mathematical modeling approach, Applied Mathematical Modelling, 103, 714-730, 2022.
- Thomas K. Torku, Abdul Q. M. Khaliq, Khaled M. Furati, Deep-Data-Driven Neural Networks for COVID-19Vaccine Efficacy, Epidemiologia, 2(4), 564–586, 2021
- K. D. Olumoyin, A. Q. M. Khaliq, K. M. Furati, Data-Driven Deep-Learning Algorithm for Asymptomatic COVID-19 Model with Varying Mitigation Measures and Transmission Rate, Epidemiologia, 2(4), 471-489, 2021.
- Jie Long, A. Q. M. Khaliq, K. M. Furati, Identification and prediction of time-varying parameters of COVID-19 model: a data-driven deep learning approach, International Journal of Computer Mathematics, 98(8), 1617-1632, 2021.
- T.A. Biala, A.Q.M. Khaliq, A fractional-order compartmental model for the Spread of the COVID-19 pandemic, Communications in Nonlinear Science and Numerical Simulation, 98, 105764, 2021.
- K.M. Furati, I.O. Sarumi, A.Q.M. Khaliq, Fractional model for the spread of COVID-19 subject to government intervention and public perception, Applied Mathematical Modelling, 95,89-105 2021.
- Ibrahim O. Sarumi, Khaled M. Furati, Abdul Q. M. Khaliq, Kassem Mustapha, Generalized Exponential Time Differencing Schemes for Stiff Fractional Systems with Non-smooth Source Term, Journal of Scientific Computing, 86:23, 2021.
- T. A. Biala, A. Q. M Khaliq, Predictor-corrector schemes for nonlinear space-fractionalparabolic PDEs with time-dependent boundary conditions, Applied Numerical Mathematics,160, 1-22. 2021.
- Muhammad Yousuf, Abdul Q. M. Khaliq, Partial differential integral equation model for pricing American option under multi state regime switching with jumps, Numerical Methods for Partial Differential Equations, (2021) https://doi.org/10.1002/num.22791
- Stefania Tomasiello, Vincenzo Loia, Abdul Khaliq, A granular recurrent neural network for multiple time series prediction, Neural Computing and Applications, 33:10293–10310, 2021.
- M.Yousuf, K.M.Furati, A.Q.M.Khaliq, High-order time-stepping methods for two-dimensional Riesz fractional nonlinear reaction–diffusion equations, Computers & Mathematics with Applications, 80(1), 204-226, 2020.
- Ibrahim O. Sarumi, Khaled M. Furati, Abdul Q. M. Khaliq, Highly Accurate Global Padé Approximations of Generalized Mittag–Leffler Function and Its Inverse, Journal of Scientific Computing, 82:46, 2020.
- Kazmi and A.Q.M. Khaliq,
*An efficient split-step method for distributed order space fractional reaction diffusion equations*, Applied Numerical Mathematics,**147**,142-160, 2020. - H.P. Bhatt, A.Q. M. Khaliq, and K.M. Furati,
*Efficient high-order compact exponential tim differencing method for space-fractional reaction-diffusion systems with nonhomogeneous boundary conditions*, Numerical Algorithms (2019)**.**https://doi.org/10.1007/s11075-019-00729-3 - Kazmi and A. Khaliq,
*A split-step predictor–corrector method for space-fractional reaction–diffusion equations with non-homogeneous boundary conditions,*Communications in Applied Mathematics and Computation,**1**(4),525-544,2019. - S.S. Alzahrani, A.Q.M .Khaliq, T.Biala, and K.M. Furati,
*Fourth-order time stepping methods with matrix transfer technique for space-fractional reaction-diffusion equations*, Applied Numerical Mathematics,**146,**123-144,2019. - S.S. Alzahrani and A.Q.M. Khaliq,
*Fourier spectral exponential time differencing methods for multi-dimensional space-fractional reaction–diffusion equations,*Journal of Computational and Applied Mathematics,**361**, 157-175, 2019. - Reshniak, A. Khaliq and D. Voss,
*Slow-scale split-step tau-leap method for stiff stochastic chemical systems,*Journal of Computational and Applied Mathematics,**361**,79–96, 2019. - S.S. Alzahrani, and A.Q.M. Khaliq,
*High-order time stepping Fourier spectral method for multi-dimensional space-fractional reaction–diffusion equations,*Computers and Mathematics with Applications,**77(3)**, 615-630, 2019 - T.A. Biala and A.Q.M. Khaliq,
*Parallel algorithms for nonlinear time–space fractional parabolic PDEs,*Journal of Computational Physics,**375,**135–154, 2018. - H.P. Bhatt A.Q.M. Khaliq, and B.A. Wade,
*Efficient Krylov-based exponential time differencing method in application to 3D advection-diffusion-reaction systems,*Applied Mathematics and Computation,**338**, 260–273, 2018. - Liang, and A.Q.M. Khaliq,
*An efficient Fourier spectral exponential time differencing method for the space-fractional nonlinear Schrödinger equations,*Computers and Mathematics with Applications,**75**, 4438–4457, 2018. - Bratsos and A Q. M. Khaliq,
*An exponential time differencing method of lines for the Burgers and the Modified Burgers equation.*Numerical Methods for Partial Differential Equations,,**34**, 2024-2039, 2018. - M.Yousuf, A.Q.M. Khaliq, and Salah Alrabeei,
*Solving complex PIDE systems for pricing American option under multi-state regime switching jump–diffusion model,*Computers and Mathematics with Applications,**75**(8), 2989-3001, 2018. - A.Q.M. Khaliq,T.A. Biala,S.S. Alzaharani, and K.M. Furati,
*Linearly implicit predictor- corrector methods for space-fractional reaction-diffusion equations with non-smooth initial data*, Computers and Mathematics with Applications,**75**(8), 2629-2657, 2018 - K.M. Furati, M. Yousuf, and A.Q.M.Khaliq,
*Fourth order methods for space fractional reaction- diffusion equations with nonsmooth data*, International Journal of Computer Mathematics,**95**(6-7), 1240-1256, 2018. - Harold A. Lay, Zane Colgin, Viktor Reshniak, Abdul Q. M. Khaliq,
*On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters,*Monte Carlo Methods and Applications,**24**(4), 309–321, 2018 - G.Tour, N.Thakoor, A.Q.M.Khaliq, and D.Y.Tangman, COS method for option pricing under a regime-switching model with time-changed Lévy processes, Quantitative Finance, 18(4), 673–692, 2018.
- O.S.Iyiola,E.O. Asante-Asamani, K.M. Furati,A.Q.M. Khaliq, and B.A. Wade,
*Efficient time discretization scheme for nonlinear space-fractional reaction diffusion equations*, International Journal of Computer Mathematics,**95**(6-7), 1274-1291, 2018. - S.Arshad, J. Huang, A.Q.M. Khaliq and Y. Tang, T
*rapezoidal scheme for time-space fractional diffusion equation with Riesz derivative*, Journal of Computational Physics,**350**(1), 1-15, 2017. - A.Q.M. Khaliq, X. Liang and K.M. Furati,
*A fourth order implicit-explicit scheme for space fractional coupled nonlinear schrödinger equations,*Numerical Algorithms,**75**(1),147-172,2017. - X.Liang, A.Q.M. Khaliq, H.Bhatt, and K.M. Furati, T
*he locally extrapolated splitting scheme fo multi-dimensioanl nonlinear space-fractional schrödinger equations,*Numerical Algorithms,**76**(4), 939-958, 2017. - I.Ahamd, S.Islam, and A.Q.M.Khaliq,
*Local RBF method for multi-dimesnional partial differentail equations*, Computers and Mathematics with applications,**72**(2),292-324,2017. - Bratsos and A.Q.M. Khaliq,
*A conservative exponential time differencing method for nonlinear**schrödinger equation, International Journal of Computer Mathematics,***94**(2),230-251, 2017. - Bhatt and A Q. M. Khaliq. A Fourth order compact scheme for reaction –diffusion systems
with non-smooth data, Journal of Computational and Applied Mathematics,
**299**, 176-193, 2016. - Bhatt and A Q M. Khaliq, Numerical simulation of coupled Burger’s equations with compact
schemes, Computer Physics communications,
**200**,117-138, 2016 - E.O.Asante-Asamani, A.Q. M. Khaliq, and B. A.Wade, A Real Distinct Poles Exponential
Time Differencing Scheme for Reaction-Diffusion Systems, Journal of Computational and Applied Mathematics,
**299**, 24-34,2016. - Yousuf, A. Q. M. Khaliq and R. Liu, Pricing American options under multi-state regime
switching with an efficient L-stable method, International Journal of Computer Mathematics,
**92**(12), 2530-2550, 2015. - Bhatt and A.Q.M. Khaliq, Locally extrapolated exponential time differencing LOD method
for multi-dimensional reaction-diffusion systems,
**285**, 256-278, 2015. - Reshniak, A. Q. M. Khaliq, D. A. Voss, and G. Zhang, Split-step methods for multi-channel
stiff stochastic differential systems, Applied Numerical Mathematics,
**89**, 1–23, 2015. - Voss and A. Q. M. Khaliq, Split–step Adams–Moulton Milstein methods for systems of
stiff stochastic differential equations, International Journal of Computer Mathematics,
**92**, 995-1011, 2015. - Liang, A.Q.M. Khaliq and Y. Xing, Fourth order exponential time differencing method
with local discontinuous Galerkin approximation for coupled nonlinear Schrödinger
equations, Commuinications in Computational Physics,
**17(2)**, 510-14 2015. - Liang, A.Q.M. Khaliq, and Q. Sheng, Exponential Time Differencing Crank-Nicolson method
with a quartic spline approximation for nonlinear Schrödinger equations, Applied Mathematics
and Computation,
**235**, 235-252, 2014 - Bhatt and A. Q. M. Khaliq, Higher order exponential time differencing scheme for system
of nonlinear Schrödinger equations, Applied Mathematics and Computation,
**228**, 271-291, 2014. - Mart´ın-Vaqueroa, A.Q.M. Khaliq, and B. Kleefeld, Stabilized explicit Runge-Kutta
method for multi-asset American options, Computers and Mathematics with Applications,
**67**(6), 1293–1308, 2014. - Yousuf, and A.Q.M. Khaliq, An efficient ETD method for pricing American options under
stochastic volatility with non-smooth payoffs, Numerical Methods for Partial Differential
Equations,
**29(**6), 1864-1880, 2013. - Q. M. Khaliq, B. Kleefeld, and R. H. Liu, Solving Complex PDE systems for pricing
American options with regime-switching by efficient exponential time differencing
schemes, Numerical Methods for Partial Differential Equations,
**29**(1), 320–336, 2013. - Sheng, and A. Q. M. Khaliq, A revisit of the semi-adaptive method for singular degenerate
reaction-diffusion equations, East Asian Journal on Applied Mathematics,
**2**(3), 185-203, 2012 - Yousuf, A. Q. M. Khaliq, and B. Kleefeld, The numerical approximation of nonlinear
Black-Scholes model for exotic path-dependent American options with transaction cost,
International Journal of Computer Mathematics,
**89**(9), 1239-1254, 2012. - Kleefeld, A. Q. M. Khaliq, and B. A. Wade, An ETD Crank-Nicolson Method for Reaction-Diffusion Systems, Numerical Methods for Partial Differential Equations,
**28**(4), 1309-1335, 2012. - 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. - 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. - 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,
**223**, 374-386, 2009. - A.Q.M. Khaliq, D.A. Voss, K. Kazmi, Adaptive θ-methods for pricing American options,
Journal of Computational and Applied Mathematics,
**222**(1), 210-227, 2008. - 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,
**10**(4), 135-142, 2008. - A.Q.M. Khaliq, D.A. Voss, M. Yousuf, Pricing Exotic Options with L-Stable Padé Schemes,
Journal of Banking and Finance,
**31**, 3438-3461, 2007. - 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,
**23**, 1249-1276, 2007. - 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,
**84**(6), 795-806, 2007. - 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,
**204**, 144-158, 2007. - 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,
**30**, 489-502, 2006. - 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,
**22**(3), 600-616, 2006 - 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,
**68**(4) 355-373, 2005. - 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,
**21**(3), 553-573, 2005. - 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)
**27**(4), 563-571, 2004. - 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, ISSN:
0302- 9743,
**2669**, 199-207, 2003. - 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. - Sheng and A.Q.M. Khaliq, Modified arc-length adaptive algorithms for degenerate reaction-diffusion
equations, Applied Mathematics and Computation,
**126**, 279-297, 2002 - 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,
**1**(1), 17-30, 2001 - Sheng, A. Q. M. Khaliq, and E. Al-Said, Solving the generalized nonlinear Schrödinger
equation via quartic spline approximations, J. of Computational Physics,
**166**(2), 400-417, 2001. - 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,
**8**, 129-148, 2001 - 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
- 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.
- D.A. Voss and A.Q.M. Khaliq, Parallel Rosenbrock Methods for Chemical Systems, Computers & Chemistry, Vol. 25(1), 101-107, 2000.
- 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
- 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
- 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.
- 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.
- A.Q.M. Khaliq and D.A.Voss, A Predictor Corrector Scheme for Reaction Diffusion Equations, ZAMM, Vol. 76(S1), 577-578, 1996.
- D.A.Voss and A.Q.M. Khaliq, Parallel LOD Methods for Multidimensional PDEs”,Computers & Math. with Applications, Vol. 30(10), 25-35, 1995
- 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.
- 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.
- 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.
- 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
- 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
- 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
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- 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.
- 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.
- H. Twizell and A. Q. M. Khaliq, One-step Multiderivative methods for first order ordinary differential equations, BIT, Vol. 21(4), 518-527, 1981