Yousuf, M.; Khaliq, A. Q. M. Pricing American option using a modified fractional Black-Scholes model under multi-state regime switching. (English) Zbl 07793177 Int. J. Theor. Appl. Finance 26, No. 4-5, Article ID 2350019, 21 p. (2023). Reviewer: Nikolay Kyurkchiev (Plovdiv) MSC: 91G60 65M06 35R11 91G20 60G40 PDFBibTeX XMLCite \textit{M. Yousuf} and \textit{A. Q. M. Khaliq}, Int. J. Theor. Appl. Finance 26, No. 4--5, Article ID 2350019, 21 p. (2023; Zbl 07793177) Full Text: DOI
Yousuf, M.; Furati, K. M.; Khaliq, A. Q. M. A hybrid fourth order time stepping method for space distributed order nonlinear reaction-diffusion equations. (English) Zbl 07783929 Comput. Math. Appl. 151, 116-126 (2023). MSC: 65M12 65M06 26A33 35R11 65M15 PDFBibTeX XMLCite \textit{M. Yousuf} et al., Comput. Math. Appl. 151, 116--126 (2023; Zbl 07783929) Full Text: DOI
Yousuf, Muhammad; Khaliq, Abdul Q. M. Partial differential integral equation model for pricing American option under multi state regime switching with jumps. (English) Zbl 07776943 Numer. Methods Partial Differ. Equations 39, No. 2, 890-912 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{M. Yousuf} and \textit{A. Q. M. Khaliq}, Numer. Methods Partial Differ. Equations 39, No. 2, 890--912 (2023; Zbl 07776943) Full Text: DOI
Sarumi, Ibrahim O.; Furati, Khaled M.; Mustapha, Kassem; Khaliq, Abdul Q. M. Efficient high-order exponential time differencing methods for nonlinear fractional differential models. (English) Zbl 1506.65094 Numer. Algorithms 92, No. 2, 1261-1288 (2023). MSC: 65L03 65L04 34K37 PDFBibTeX XMLCite \textit{I. O. Sarumi} et al., Numer. Algorithms 92, No. 2, 1261--1288 (2023; Zbl 1506.65094) Full Text: DOI
Feng, Lin; Chen, Ziren; Lay, Harold A. jun.; Furati, Khaled; Khaliq, Abdul Data driven time-varying SEIR-LSTM/GRU algorithms to track the spread of COVID-19. (English) Zbl 1508.92254 Math. Biosci. Eng. 19, No. 9, 8935-8962 (2022). MSC: 92D30 PDFBibTeX XMLCite \textit{L. Feng} et al., Math. Biosci. Eng. 19, No. 9, 8935--8962 (2022; Zbl 1508.92254) Full Text: DOI
Chen, Ziren; Feng, Lin; Lay, Harold A.; Furati, Khaled; Khaliq, Abdul SEIR model with unreported infected population and dynamic parameters for the spread of COVID-19. (English) Zbl 07529651 Math. Comput. Simul. 198, 31-46 (2022). MSC: 92-XX 91-XX PDFBibTeX XMLCite \textit{Z. Chen} et al., Math. Comput. Simul. 198, 31--46 (2022; Zbl 07529651) Full Text: DOI Link
Sarumi, Ibrahim O.; Furati, Khaled M.; Khaliq, Abdul Q. M.; Mustapha, Kassem Generalized exponential time differencing schemes for stiff fractional systems with nonsmooth source term. (English) Zbl 1469.65115 J. Sci. Comput. 86, No. 2, Paper No. 23, 22 p. (2021). MSC: 65L04 34A08 92C45 PDFBibTeX XMLCite \textit{I. O. Sarumi} et al., J. Sci. Comput. 86, No. 2, Paper No. 23, 22 p. (2021; Zbl 1469.65115) Full Text: DOI
Biala, T. A.; Khaliq, Abdul Q. M. Predictor-corrector schemes for nonlinear space-fractional parabolic PDEs with time-dependent boundary conditions. (English) Zbl 1460.65111 Appl. Numer. Math. 160, 1-22 (2021). Reviewer: Abdallah Bradji (Annaba) MSC: 65M22 65M06 65N06 65D32 65L10 41A21 35R11 65M15 PDFBibTeX XMLCite \textit{T. A. Biala} and \textit{A. Q. M. Khaliq}, Appl. Numer. Math. 160, 1--22 (2021; Zbl 1460.65111) Full Text: DOI
Yousuf, M.; Furati, K. M.; Khaliq, Abdul Q. M. High-order time-stepping methods for two-dimensional Riesz fractional nonlinear reaction-diffusion equations. (English) Zbl 1446.65083 Comput. Math. Appl. 80, No. 1, 204-226 (2020). MSC: 65M06 65M12 65L06 35Q74 35Q92 92C45 PDFBibTeX XMLCite \textit{M. Yousuf} et al., Comput. Math. Appl. 80, No. 1, 204--226 (2020; Zbl 1446.65083) Full Text: DOI
Bhatt, H. P.; Khaliq, A. Q. M.; Furati, K. M. Efficient high-order compact exponential time differencing method for space-fractional reaction-diffusion systems with nonhomogeneous boundary conditions. (English) Zbl 1437.65089 Numer. Algorithms 83, No. 4, 1373-1397 (2020). MSC: 65M06 65F05 26A33 35R11 35K57 80A32 35Q79 65M12 65M15 PDFBibTeX XMLCite \textit{H. P. Bhatt} et al., Numer. Algorithms 83, No. 4, 1373--1397 (2020; Zbl 1437.65089) Full Text: DOI
Sarumi, Ibrahim O.; Furati, Khaled M.; Khaliq, Abdul Q. M. Highly accurate global Padé approximations of generalized Mittag-Leffler function and its inverse. (English) Zbl 1440.65100 J. Sci. Comput. 82, No. 2, Paper No. 46, 27 p. (2020). MSC: 65M06 33E12 41A21 35C20 26A33 35R11 74F10 74K20 35Q74 PDFBibTeX XMLCite \textit{I. O. Sarumi} et al., J. Sci. Comput. 82, No. 2, Paper No. 46, 27 p. (2020; Zbl 1440.65100) Full Text: DOI arXiv
Kazmi, Kamran; Khaliq, Abdul Q. M. An efficient split-step method for distributed-order space-fractional reaction-diffusion equations with time-dependent boundary conditions. (English) Zbl 1434.65122 Appl. Numer. Math. 147, 142-160 (2020). MSC: 65M06 65L06 35R11 26A33 60H10 76D05 PDFBibTeX XMLCite \textit{K. Kazmi} and \textit{A. Q. M. Khaliq}, Appl. Numer. Math. 147, 142--160 (2020; Zbl 1434.65122) Full Text: DOI
Alzahrani, S. S.; Khaliq, Abdul Q. M. High-order time stepping Fourier spectral method for multi-dimensional space-fractional reaction-diffusion equations. (English) Zbl 1442.65289 Comput. Math. Appl. 77, No. 3, 615-630 (2019). MSC: 65M70 65M12 35R11 PDFBibTeX XMLCite \textit{S. S. Alzahrani} and \textit{A. Q. M. Khaliq}, Comput. Math. Appl. 77, No. 3, 615--630 (2019; Zbl 1442.65289) Full Text: DOI
Alzahrani, S. S.; Khaliq, A. Q. M.; Biala, T. A.; Furati, K. M. Fourth-order time stepping methods with matrix transfer technique for space-fractional reaction-diffusion equations. (English) Zbl 1431.65194 Appl. Numer. Math. 146, 123-144 (2019). Reviewer: Abdallah Bradji (Annaba) MSC: 65M99 65L06 35R11 41A21 65M12 65M06 35P10 PDFBibTeX XMLCite \textit{S. S. Alzahrani} et al., Appl. Numer. Math. 146, 123--144 (2019; Zbl 1431.65194) Full Text: DOI
Alzahrani, S. S.; Khaliq, A. Q. M. Fourier spectral exponential time differencing methods for multi-dimensional space-fractional reaction-diffusion equations. (English) Zbl 1422.65276 J. Comput. Appl. Math. 361, 157-175 (2019). MSC: 65M70 65N35 65M06 65L06 41A21 35R11 PDFBibTeX XMLCite \textit{S. S. Alzahrani} and \textit{A. Q. M. Khaliq}, J. Comput. Appl. Math. 361, 157--175 (2019; Zbl 1422.65276) Full Text: DOI
Bratsos, A. G.; Khaliq, A. Q. M. An exponential time differencing method of lines for Burgers-Fisher and coupled Burgers equations. (English) Zbl 1524.65320 J. Comput. Appl. Math. 356, 182-197 (2019). MSC: 65M06 35Q53 65M70 65M20 65L06 65H10 65F60 PDFBibTeX XMLCite \textit{A. G. Bratsos} and \textit{A. Q. M. Khaliq}, J. Comput. Appl. Math. 356, 182--197 (2019; Zbl 1524.65320) Full Text: DOI
Iyiola, O. S.; Asante-Asamani, E. O.; Furati, K. M.; Khaliq, A. Q. M.; Wade, B. A. Efficient time discretization scheme for nonlinear space fractional reaction-diffusion equations. (English) Zbl 1499.65395 Int. J. Comput. Math. 95, No. 6-7, 1274-1291 (2018). MSC: 65M06 35K57 35R11 65M20 PDFBibTeX XMLCite \textit{O. S. Iyiola} et al., Int. J. Comput. Math. 95, No. 6--7, 1274--1291 (2018; Zbl 1499.65395) Full Text: DOI
Furati, Khaled M.; Yousuf, M.; Khaliq, A. Q. M. Fourth-order methods for space fractional reaction-diffusion equations with non-smooth data. (English) Zbl 1499.35637 Int. J. Comput. Math. 95, No. 6-7, 1240-1256 (2018). MSC: 35R11 65N12 65N06 35B65 35B30 PDFBibTeX XMLCite \textit{K. M. Furati} et al., Int. J. Comput. Math. 95, No. 6--7, 1240--1256 (2018; Zbl 1499.35637) Full Text: DOI
Biala, T. A.; Khaliq, A. Q. M. Parallel algorithms for nonlinear time-space fractional parabolic PDEs. (English) Zbl 1416.65303 J. Comput. Phys. 375, 135-154 (2018). MSC: 65M12 35R11 65M15 65Y05 PDFBibTeX XMLCite \textit{T. A. Biala} and \textit{A. Q. M. Khaliq}, J. Comput. Phys. 375, 135--154 (2018; Zbl 1416.65303) Full Text: DOI
Liang, Xiao; Khaliq, Abdul Q. M. An efficient Fourier spectral exponential time differencing method for the space-fractional nonlinear Schrödinger equations. (English) Zbl 1419.65083 Comput. Math. Appl. 75, No. 12, 4438-4457 (2018). MSC: 65M70 65M12 35R11 35Q55 35Q41 65M06 PDFBibTeX XMLCite \textit{X. Liang} and \textit{A. Q. M. Khaliq}, Comput. Math. Appl. 75, No. 12, 4438--4457 (2018; Zbl 1419.65083) Full Text: DOI
Yousuf, M.; Khaliq, Abdul Q. M.; Alrabeei, Salah Solving complex PIDE systems for pricing American option under multi-state regime switching jump-diffusion model. (English) Zbl 1415.91322 Comput. Math. Appl. 75, No. 8, 2989-3001 (2018). MSC: 91G60 65M06 91G20 60G40 60J75 65M12 PDFBibTeX XMLCite \textit{M. Yousuf} et al., Comput. Math. Appl. 75, No. 8, 2989--3001 (2018; Zbl 1415.91322) Full Text: DOI
Lay, Harold A.; Colgin, Zane; Reshniak, Viktor; Khaliq, Abdul Q. M. On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters. (English) Zbl 1405.65015 Monte Carlo Methods Appl. 24, No. 4, 309-321 (2018). MSC: 65C30 65Y10 91G30 PDFBibTeX XMLCite \textit{H. A. Lay} et al., Monte Carlo Methods Appl. 24, No. 4, 309--321 (2018; Zbl 1405.65015) Full Text: DOI
Arshad, Sadia; Huang, Jianfei; Khaliq, Abdul Q. M.; Tang, Yifa Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative. (English) Zbl 1380.65141 J. Comput. Phys. 350, 1-15 (2017). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{S. Arshad} et al., J. Comput. Phys. 350, 1--15 (2017; Zbl 1380.65141) Full Text: DOI
Ahmad, Imtiaz; Siraj-ul-Islam; Khaliq, Abdul Q. M. Local RBF method for multi-dimensional partial differential equations. (English) Zbl 1375.65136 Comput. Math. Appl. 74, No. 2, 292-324 (2017). MSC: 65M70 35Q53 35K57 91G60 PDFBibTeX XMLCite \textit{I. Ahmad} et al., Comput. Math. Appl. 74, No. 2, 292--324 (2017; Zbl 1375.65136) Full Text: DOI
Bratsos, A. G.; Khaliq, A. Q. M. A conservative exponential time differencing method for the nonlinear cubic Schrödinger equation. (English) Zbl 1364.65159 Int. J. Comput. Math. 94, No. 2, 230-251 (2017). MSC: 65M06 35K55 35Q41 65M20 PDFBibTeX XMLCite \textit{A. G. Bratsos} and \textit{A. Q. M. Khaliq}, Int. J. Comput. Math. 94, No. 2, 230--251 (2017; Zbl 1364.65159) Full Text: DOI
Khaliq, A. Q. M.; Liang, X.; Furati, K. M. A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrödinger equations. (English) Zbl 1365.65195 Numer. Algorithms 75, No. 1, 147-172 (2017). MSC: 65M06 35R11 35Q55 65M12 PDFBibTeX XMLCite \textit{A. Q. M. Khaliq} et al., Numer. Algorithms 75, No. 1, 147--172 (2017; Zbl 1365.65195) Full Text: DOI
Bhatt, H. P.; Khaliq, A. Q. M. Fourth-order compact schemes for the numerical simulation of coupled Burgers’ equation. (English) Zbl 1351.35167 Comput. Phys. Commun. 200, 117-138 (2016). MSC: 35Q53 65M06 PDFBibTeX XMLCite \textit{H. P. Bhatt} and \textit{A. Q. M. Khaliq}, Comput. Phys. Commun. 200, 117--138 (2016; Zbl 1351.35167) Full Text: DOI
Bhatt, H. P.; Khaliq, A. Q. M. A compact fourth-order \(L\)-stable scheme for reaction-diffusion systems with nonsmooth data. (English) Zbl 1382.65234 J. Comput. Appl. Math. 299, 176-193 (2016). MSC: 65M06 65L06 65M20 PDFBibTeX XMLCite \textit{H. P. Bhatt} and \textit{A. Q. M. Khaliq}, J. Comput. Appl. Math. 299, 176--193 (2016; Zbl 1382.65234) Full Text: DOI
Asante-Asamani, E. O.; Khaliq, A. Q. M.; Wade, B. A. A real distinct poles exponential time differencing scheme for reaction-diffusion systems. (English) Zbl 1333.65106 J. Comput. Appl. Math. 299, 24-34 (2016). MSC: 65M38 35K57 35K58 65M12 PDFBibTeX XMLCite \textit{E. O. Asante-Asamani} et al., J. Comput. Appl. Math. 299, 24--34 (2016; Zbl 1333.65106) Full Text: DOI
Yousuf, M.; Khaliq, A. Q. M.; Liu, R. H. Pricing American options under multi-state regime switching with an efficient \(L\)-stable method. (English) Zbl 1386.91168 Int. J. Comput. Math. 92, No. 12, 2530-2550 (2015). MSC: 91G60 65M06 65M12 65M15 91G20 60G40 PDFBibTeX XMLCite \textit{M. Yousuf} et al., Int. J. Comput. Math. 92, No. 12, 2530--2550 (2015; Zbl 1386.91168) Full Text: DOI
Voss, David A.; Khaliq, Abdul Q. M. Split-step Adams-Moulton Milstein methods for systems of stiff stochastic differential equations. (English) Zbl 1316.60100 Int. J. Comput. Math. 92, No. 5, 995-1011 (2015). MSC: 60H10 60H35 65C30 65L06 65L20 PDFBibTeX XMLCite \textit{D. A. Voss} and \textit{A. Q. M. Khaliq}, Int. J. Comput. Math. 92, No. 5, 995--1011 (2015; Zbl 1316.60100) Full Text: DOI
Reshniak, V.; Khaliq, A. Q. M.; Voss, D. A.; Zhang, G. Split-step Milstein methods for multi-channel stiff stochastic differential systems. (English) Zbl 1306.65008 Appl. Numer. Math. 89, 1-23 (2015). MSC: 65C30 60H10 60H35 34F05 65L04 65L20 PDFBibTeX XMLCite \textit{V. Reshniak} et al., Appl. Numer. Math. 89, 1--23 (2015; Zbl 1306.65008) Full Text: DOI arXiv
Bhatt, Harish P.; Khaliq, Abdul Q. M. Higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations. (English) Zbl 1364.78033 Appl. Math. Comput. 228, 271-291 (2014). MSC: 78M20 78A10 35Q55 65M06 PDFBibTeX XMLCite \textit{H. P. Bhatt} and \textit{A. Q. M. Khaliq}, Appl. Math. Comput. 228, 271--291 (2014; Zbl 1364.78033) Full Text: DOI
Liang, Xiao; Khaliq, Abdul Q. M.; Sheng, Qin Exponential time differencing Crank-Nicolson method with a quartic spline approximation for nonlinear Schrödinger equations. (English) Zbl 1334.65134 Appl. Math. Comput. 235, 235-252 (2014). MSC: 65M06 35Q55 65M12 PDFBibTeX XMLCite \textit{X. Liang} et al., Appl. Math. Comput. 235, 235--252 (2014; Zbl 1334.65134) Full Text: DOI
Khaliq, A. Q. M.; Kleefeld, B.; Liu, R. H. Solving complex PDE systems for pricing American options with regime-switching by efficient exponential time differencing schemes. (English) Zbl 1282.91377 Numer. Methods Partial Differ. Equations 29, No. 1, 320-336 (2013). MSC: 91G60 91G20 35Q91 65M06 60J27 60J60 65M20 PDFBibTeX XMLCite \textit{A. Q. M. Khaliq} et al., Numer. Methods Partial Differ. Equations 29, No. 1, 320--336 (2013; Zbl 1282.91377) Full Text: DOI
Yousuf, M.; Khaliq, A. Q. M.; Kleefeld, B. The numerical approximation of nonlinear Black–Scholes model for exotic path-dependent American options with transaction cost. (English) Zbl 1255.91434 Int. J. Comput. Math. 89, No. 9, 1239-1254 (2012). MSC: 91G60 65M12 65M15 65Y05 65Y20 PDFBibTeX XMLCite \textit{M. Yousuf} et al., Int. J. Comput. Math. 89, No. 9, 1239--1254 (2012; Zbl 1255.91434) Full Text: DOI
Khaliq, A. Q. M.; Martín-Vaquero, J.; Wade, B. A.; Yousuf, M. Smoothing schemes for reaction-diffusion systems with nonsmooth data. (English) Zbl 1155.65062 J. Comput. Appl. Math. 223, No. 1, 374-386 (2009). MSC: 65M06 PDFBibTeX XMLCite \textit{A. Q. M. Khaliq} et al., J. Comput. Appl. Math. 223, No. 1, 374--386 (2009; Zbl 1155.65062) Full Text: DOI
Sheng, Q.; Khaliq, A. Q. M.; Al-Said, E. A. Solving the generalized nonlinear Schrödinger equation via quartic spline approximation. (English) Zbl 0979.65082 J. Comput. Phys. 166, No. 2, 400-417 (2001). Reviewer: Willy Govaerts (Gent) MSC: 65M20 65M12 65M70 35Q55 35Q51 PDFBibTeX XMLCite \textit{Q. Sheng} et al., J. Comput. Phys. 166, No. 2, 400--417 (2001; Zbl 0979.65082) Full Text: DOI
Khaliq, A. Q. M.; Abukhodair, B.; Sheng, Q.; Ismail, M. S. A predictor-corrector scheme for the sine-Gordon equation. (English) Zbl 0951.65089 Numer. Methods Partial Differ. Equations 16, No. 2, 133-146 (2000). Reviewer: V.P.Tyagi (Bombay) MSC: 65M20 65M12 65L20 65L06 34A34 35Q53 PDFBibTeX XMLCite \textit{A. Q. M. Khaliq} et al., Numer. Methods Partial Differ. Equations 16, No. 2, 133--146 (2000; Zbl 0951.65089) Full Text: DOI
Khaliq, A. Q. M. A predictor-corrector scheme for fourth order parabolic partial differential equations. (English) Zbl 0688.65059 Comput. Math. Appl. 17, No. 12, 1563-1566 (1989). Reviewer: F.Ribiere-Michaud MSC: 65N06 74H45 74K10 35K35 PDFBibTeX XMLCite \textit{A. Q. M. Khaliq}, Comput. Math. Appl. 17, No. 12, 1563--1566 (1989; Zbl 0688.65059) Full Text: DOI
Khaliq, A. Q. M.; Twizell, E. H. Backward difference replacements of the space derivative in first-order hyperbolic equations. (English) Zbl 0522.65062 Comput. Methods Appl. Mech. Eng. 43, 45-56 (1984). MSC: 65N12 65N22 35L50 PDFBibTeX XMLCite \textit{A. Q. M. Khaliq} and \textit{E. H. Twizell}, Comput. Methods Appl. Mech. Eng. 43, 45--56 (1984; Zbl 0522.65062) Full Text: DOI
Twizell, E. H.; Khaliq, A. Q. M. A difference scheme with high accuracy in time for fourth-order parabolic equations. (English) Zbl 0509.65044 Comput. Methods Appl. Mech. Eng. 41, 91-104 (1983). MSC: 65N06 65N12 74K10 74H45 35K35 PDFBibTeX XMLCite \textit{E. H. Twizell} and \textit{A. Q. M. Khaliq}, Comput. Methods Appl. Mech. Eng. 41, 91--104 (1983; Zbl 0509.65044) Full Text: DOI