TY - JOUR AU - Ajello, W. G. AU - Freedman, H. I. AU - Wu, J. PY - 1992 DA - 1992// TI - A model of stage structured population growth with density depended time delay JO - SIAM J. Appl. Math. VL - 52 UR - https://doi.org/10.1137/0152048 DO - 10.1137/0152048 ID - Ajello1992 ER - TY - JOUR AU - Akkaya, T. AU - Yalcinbas, S. AU - Sezer, M. PY - 2013 DA - 2013// TI - Numeric solutions for the pantograph type delay differential equation using first Boubaker polynomials JO - Appl. Math. Comput. VL - 219 ID - Akkaya2013 ER - TY - JOUR AU - Akyuz-Dascioglu, A. AU - Sezer, M. PY - 2015 DA - 2015// TI - Bernoulli collocation method for high-order generalized pantograph equations JO - New Trends Math. Sci. VL - 3 ID - Akyuz-Dascioglu2015 ER - TY - JOUR AU - Bahşi, M. M. AU - Çevik, M. PY - 2015 DA - 2015// TI - Numerical solution of pantograph-type delay differential equations using perturbation-iteration algorithms JO - J. Appl. Math. VL - 2015 UR - https://doi.org/10.1155/2015/139821 DO - 10.1155/2015/139821 ID - Bahşi2015 ER - TY - JOUR AU - Bahşi, M. M. AU - Çevik, M. AU - Sezer, M. PY - 2015 DA - 2015// TI - Orthoexponential polynomial solutions of delay pantograph differential equations with residual error estimation JO - Math. Comput. VL - 271 ID - Bahşi2015 ER - TY - JOUR AU - Buhmann, M. AU - Iserles, A. PY - 1993 DA - 1993// TI - Stability of the discretized pantograph differential equation JO - Math. Comput. VL - 60 UR - https://doi.org/10.1090/S0025-5718-1993-1176707-2 DO - 10.1090/S0025-5718-1993-1176707-2 ID - Buhmann1993 ER - TY - BOOK AU - Canuto, C. AU - Hussaini, M. Y. AU - Quarteroni, A. AU - Zang, T. A. PY - 1988 DA - 1988// TI - Spectral Method in Fluid Dynamics PB - Springer CY - New York UR - https://doi.org/10.1007/978-3-642-84108-8 DO - 10.1007/978-3-642-84108-8 ID - Canuto1988 ER - TY - JOUR AU - Doha, E. H. AU - Bhrawy, A. H. AU - Baleanu, D. AU - Hafez, R. M. PY - 2014 DA - 2014// TI - A new Jacobi rational-Gauss collocation method for numerical solution of generalized pantograph equations JO - Appl. Numer. Math. VL - 77 UR - https://doi.org/10.1016/j.apnum.2013.11.003 DO - 10.1016/j.apnum.2013.11.003 ID - Doha2014 ER - TY - JOUR AU - Fox, L. AU - Mayers, D. F. AU - Ockendon, J. A. AU - Tayler, A. B. PY - 1971 DA - 1971// TI - On a functional differential equation JO - J. Inst. Math. Appl. VL - 8 UR - https://doi.org/10.1093/imamat/8.3.271 DO - 10.1093/imamat/8.3.271 ID - Fox1971 ER - TY - BOOK AU - Freud, G. PY - 1971 DA - 1971// TI - Orthogonal Polynomials PB - Pergamom Press CY - Elmsford ID - Freud1971 ER - TY - JOUR AU - Ghaznavi, M. AU - Noori Skandari, M. H. PY - 2018 DA - 2018// TI - An efficient pseudo-spectral method for nonsmooth dynamical systems JO - Iran. J. Sci. Technol., Trans. a Sci. VL - 42 UR - https://doi.org/10.1007/s40995-016-0040-9 DO - 10.1007/s40995-016-0040-9 ID - Ghaznavi2018 ER - TY - JOUR AU - Guglielmi, N. AU - Zennaro, M. PY - 2003 DA - 2003// TI - Stability of one-leg θ-methods for the variable coefficient pantograph equation on the quasi-geometric mesh JO - IMA J. Numer. Anal. VL - 23 UR - https://doi.org/10.1093/imanum/23.3.421 DO - 10.1093/imanum/23.3.421 ID - Guglielmi2003 ER - TY - JOUR AU - Huang, Q. AU - Xie, H. AU - Brunner, H. PY - 2011 DA - 2011// TI - Superconvergence of discontinuous Galerkin solutions for delay differential equations of pantograph type JO - SIAM J. Sci. Comput. VL - 33 UR - https://doi.org/10.1137/110824632 DO - 10.1137/110824632 ID - Huang2011 ER - TY - JOUR AU - Huang, Q. AU - Xu, X. AU - Brunner, H. PY - 2016 DA - 2016// TI - Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type JO - Discrete Contin. Dyn. Syst. VL - 36 UR - https://doi.org/10.3934/dcds.2016039 DO - 10.3934/dcds.2016039 ID - Huang2016 ER - TY - JOUR AU - Huang, Y. AU - Mohammadizadeh, F. AU - Noori Skandari, M. H. AU - Tehrani, H. A. AU - Tohidi, E. PY - 2020 DA - 2020// TI - Space–time Chebyshev spectral collocation method for nonlinear time–fractional Burgers equations based on efficient basis functions JO - Math. Methods Appl. Sci. UR - https://doi.org/10.1002/mma.7015 DO - 10.1002/mma.7015 ID - Huang2020 ER - TY - JOUR AU - Hwang, C. AU - Shih, Y. P. PY - 1982 DA - 1982// TI - Laguerre series solution of a functional differential equation JO - Int. J. Syst. Sci. VL - 13 UR - https://doi.org/10.1080/00207728208926388 DO - 10.1080/00207728208926388 ID - Hwang1982 ER - TY - JOUR AU - Ishtiaq, A. AU - Hermann, B. AU - Tao, T. PY - 2009 DA - 2009// TI - A spectral method for pantograph-type delay differential equations and its convergence analysis JO - J. Comput. Math. VL - 27 ID - Ishtiaq2009 ER - TY - JOUR AU - Isik, O. R. AU - Guney, Z. AU - Sezer, M. PY - 2012 DA - 2012// TI - Bernstein series solutions of pantograph equations using polynomial interpolation JO - J. Differ. Equ. Appl. VL - 18 UR - https://doi.org/10.1080/10236198.2010.496456 DO - 10.1080/10236198.2010.496456 ID - Isik2012 ER - TY - JOUR AU - Isik, O. R. AU - Turkoglu, T. PY - 2016 DA - 2016// TI - A rational approximate solution for generalized pantograph-delay differential equations JO - Math. Methods Appl. Sci. VL - 39 UR - https://doi.org/10.1002/mma.3616 DO - 10.1002/mma.3616 ID - Isik2016 ER - TY - JOUR AU - Javadi, S. AU - Babolian, E. AU - Taheri, Z. PY - 2016 DA - 2016// TI - Solving generalized pantograph equations by shifted orthonormal Bernstein polynomials JO - J. Comput. Appl. Math. UR - https://doi.org/10.1016/j.cam.2016.02.025 DO - 10.1016/j.cam.2016.02.025 ID - Javadi2016 ER - TY - JOUR AU - Milosevic, M. AU - Jovanovic, M. PY - 2011 DA - 2011// TI - A Taylor polynomial approach in approximations of solution to pantograph stochastic differential equations with Markovian switching JO - Math. Comput. Model. VL - 53 UR - https://doi.org/10.1016/j.mcm.2010.08.016 DO - 10.1016/j.mcm.2010.08.016 ID - Milosevic2011 ER - TY - JOUR AU - Noori Skandari, M. H. AU - Ghaznavi, M. PY - 2018 DA - 2018// TI - A novel technique for a class of singular boundary value problems JO - Comput. Methods Differ. Equ. VL - 6 ID - Noori Skandari2018 ER - TY - JOUR AU - Ockendon, J. R. AU - Tayler, A. B. PY - 1971 DA - 1971// TI - The dynamics of a current collection system for an electric locomotive JO - Proc. R. Soc. Lond. A VL - 322 UR - https://doi.org/10.1098/rspa.1971.0078 DO - 10.1098/rspa.1971.0078 ID - Ockendon1971 ER - TY - JOUR AU - Olvera, D. AU - Elias-Zuniga, A. AU - Lopez de Lacalle, L. N. AU - Rodriguez, C. A. PY - 2015 DA - 2015// TI - Approximate solutions of delay differential equations with constant and variable coefficients by the enhanced multistage homotopy perturbation method JO - Abstr. Appl. Anal. VL - 2015 UR - https://doi.org/10.1155/2015/382475 DO - 10.1155/2015/382475 ID - Olvera2015 ER - TY - JOUR AU - Peykrayegan, N. AU - Ghovatmand, M. AU - Noori Skandari, M. H. PY - 2021 DA - 2021// TI - On the convergence of Jacobi–Gauss collocation method for linear fractional delay differential equations JO - Math. Methods Appl. Sci. VL - 44 UR - https://doi.org/10.1002/mma.6934 DO - 10.1002/mma.6934 ID - Peykrayegan2021 ER - TY - JOUR AU - Rao, G. P. AU - Palanisamy, K. R. PY - 1982 DA - 1982// TI - Walsh stretch matrices and functional differential equation JO - IEEE Trans. Autom. Control VL - 27 UR - https://doi.org/10.1109/TAC.1982.1102858 DO - 10.1109/TAC.1982.1102858 ID - Rao1982 ER - TY - JOUR AU - Reutskiy, S. Y. PY - 2015 DA - 2015// TI - A new collocation method for approximate solution of the pantograph functional differential equations with proportional delay JO - Appl. Math. Comput. VL - 266 ID - Reutskiy2015 ER - TY - JOUR AU - Saadatmandi, A. AU - Dehghan, M. PY - 2006 DA - 2006// TI - A tau method for the one-dimensional parabolic inverse problem subject to temperature over specification JO - Comput. Math. Appl. VL - 52 UR - https://doi.org/10.1016/j.camwa.2006.04.017 DO - 10.1016/j.camwa.2006.04.017 ID - Saadatmandi2006 ER - TY - JOUR AU - Saadatmandi, A. AU - Dehghan, M. PY - 2009 DA - 2009// TI - Variational iteration method for solving a generalized pantograph equation JO - Comput. Math. Appl. VL - 58 UR - https://doi.org/10.1016/j.camwa.2009.03.017 DO - 10.1016/j.camwa.2009.03.017 ID - Saadatmandi2009 ER - TY - JOUR AU - Sedaghat, S. AU - Ordokhani, Y. AU - Dehghan, M. PY - 2012 DA - 2012// TI - Numerical solution of the delay differential equations of pantograph type via Chebyshev polynomials JO - Commun. Nonlinear Sci. Numer. Simul. VL - 17 UR - https://doi.org/10.1016/j.cnsns.2012.05.009 DO - 10.1016/j.cnsns.2012.05.009 ID - Sedaghat2012 ER - TY - JOUR AU - Sezer, M. AU - Akyüz-Daşcıoğlu, A. PY - 2007 DA - 2007// TI - A Taylor method for numerical solution of generalized pantograph equations with linear functional argument JO - J. Comput. Appl. Math. VL - 200 UR - https://doi.org/10.1016/j.cam.2005.12.015 DO - 10.1016/j.cam.2005.12.015 ID - Sezer2007 ER - TY - JOUR AU - Sezer, M. AU - Yalçinbaş, S. AU - Gulsu, M. PY - 2008 DA - 2008// TI - A Taylor polynomial approach for solving generalized pantograph equations with nonhomogeneous term JO - Int. J. Comput. Math. VL - 85 UR - https://doi.org/10.1080/00207160701466784 DO - 10.1080/00207160701466784 ID - Sezer2008 ER - TY - BOOK AU - Shen, J. AU - Tang, T. AU - Wang, L. L. PY - 2011 DA - 2011// TI - Spectral Methods Algorithms, Analysis and Applications PB - Springer CY - Berlin ID - Shen2011 ER - TY - JOUR AU - Tohidi, E. AU - Bhrawy, A. H. AU - Erfani, K. PY - 2013 DA - 2013// TI - A collocation method based on Bernoulli operational matrix for numerical solution of generalized pantograph equation JO - Appl. Math. Model. VL - 37 UR - https://doi.org/10.1016/j.apm.2012.09.032 DO - 10.1016/j.apm.2012.09.032 ID - Tohidi2013 ER - TY - BOOK AU - Trefethen, L. N. PY - 2000 DA - 2000// TI - Spectral Methods in MATLAB PB - SIAM CY - Philadelphia UR - https://doi.org/10.1137/1.9780898719598 DO - 10.1137/1.9780898719598 ID - Trefethen2000 ER - TY - JOUR AU - Trif, D. PY - 2012 DA - 2012// TI - Direct operational tau method for pantograph-type equations JO - Appl. Math. Comput. VL - 219 ID - Trif2012 ER - TY - JOUR AU - Turkyilmazoglu, M. PY - 2014 DA - 2014// TI - An effective approach for numerical solutions of high-order Fredholm integro-differential equations JO - Appl. Math. Comput. VL - 227 ID - Turkyilmazoglu2014 ER - TY - JOUR AU - Turkyilmazoglu, M. PY - 2017 DA - 2017// TI - Solution of initial and boundary value problems by an effective accurate method JO - Int. J. Comput. Methods VL - 14 UR - https://doi.org/10.1142/S0219876217500694 DO - 10.1142/S0219876217500694 ID - Turkyilmazoglu2017 ER - TY - JOUR AU - Turkyilmazoglu, M. PY - 2018 DA - 2018// TI - Convergence accelerating in the homotopy analysis method: a new approach JO - Adv. Appl. Math. Mech. VL - 10 UR - https://doi.org/10.4208/aamm.OA-2017-0196 DO - 10.4208/aamm.OA-2017-0196 ID - Turkyilmazoglu2018 ER - TY - JOUR AU - Turkyilmazoglu, M. PY - 2019 DA - 2019// TI - Accelerating the convergence of decomposition method of Adomian JO - J. Comput. Sci. VL - 31 UR - https://doi.org/10.1016/j.jocs.2018.12.014 DO - 10.1016/j.jocs.2018.12.014 ID - Turkyilmazoglu2019 ER - TY - JOUR AU - Wang, W. PY - 2015 DA - 2015// TI - High order stable Runge–Kutta methods for nonlinear generalized pantograph equations on the geometric mesh JO - Appl. Math. Model. VL - 39 UR - https://doi.org/10.1016/j.apm.2014.05.019 DO - 10.1016/j.apm.2014.05.019 ID - Wang2015 ER - TY - JOUR AU - Xu, X. AU - Huang, Q. AU - Chen, H. PY - 2016 DA - 2016// TI - Local superconvergence of continuous Galerkin solutions for delay differential equations of pantograph type JO - J. Comput. Math. VL - 33 UR - https://doi.org/10.4208/jcm.1511-m2014-0216 DO - 10.4208/jcm.1511-m2014-0216 ID - Xu2016 ER - TY - JOUR AU - Yalcinbas, S. AU - Aynigul, M. AU - Sezer, M. PY - 2011 DA - 2011// TI - A collocation method using Hermite polynomials for approximate solution of pantograph equations JO - J. Franklin Inst. VL - 348 UR - https://doi.org/10.1016/j.jfranklin.2011.05.003 DO - 10.1016/j.jfranklin.2011.05.003 ID - Yalcinbas2011 ER - TY - JOUR AU - Yang, C. PY - 2018 DA - 2018// TI - Modified Chebyshev collocation method for pantograph-type differential equations JO - Appl. Numer. Math. VL - 134 UR - https://doi.org/10.1016/j.apnum.2018.08.002 DO - 10.1016/j.apnum.2018.08.002 ID - Yang2018 ER - TY - JOUR AU - Yuzbasi, S. AU - Sezer, M. PY - 2013 DA - 2013// TI - An exponential approximation for solutions of generalized pantograph-delay differential equations JO - Appl. Math. Model. VL - 37 UR - https://doi.org/10.1016/j.apm.2013.04.028 DO - 10.1016/j.apm.2013.04.028 ID - Yuzbasi2013 ER - TY - JOUR AU - Zhang, G. AU - Xiao, A. AU - Wang, W. PY - 2016 DA - 2016// TI - The asymptotic behaviour of the θ-methods with constant stepsize for the generalized pantograph equation JO - Int. J. Comput. Math. VL - 93 UR - https://doi.org/10.1080/00207160.2015.1061124 DO - 10.1080/00207160.2015.1061124 ID - Zhang2016 ER - TY - JOUR AU - Zhao, J. J. AU - Xu, Y. AU - Wang, H. X. AU - Liu, M. Z. PY - 2006 DA - 2006// TI - Stability of a class of Runge–Kutta methods for a family of pantograph equations of neutral type JO - Appl. Math. Comput. VL - 181 ID - Zhao2006 ER -