Payam Mokhtary, PhD Personal:
Name: Payam Mokhtary
Current Official Address:
Department of Mathematics, Faculty of Basic Sciences,
Sahand university of Technology, Sahand NewTown, Tabriz, Iran.
Tel: 04133459040 Education:
PhD: Applied Mathematics (Numerical Analysis), K. N. Toosi university of Technology, Tehran, Iran. (200813)
M.sc: Applied Mathematics (Numerical Analysis), University of Tarbiat Modaress, Tehran, Iran. (200608)
B.sc: Pure mathematics, University of Urmia, Urmia, Iran. (200206)
Teaching Experience:
 Approximation Theory (Graduate Level)
 Numerical Solution of Ordinary differential Equations (Graduate Level)
 Fractional Differential Equations (Graduate Level)  Numerical Solution of Integral Equations (Graduate Level)  Numerical Methods in Linear Algebra (Graduate Level)
 Advanced Numerical Analysis (Graduate Level)
 Mathematics Laboratory (Graduate Level)  Advance Engineering Mathematics (Graduate and Under Graduate Levels)  Differential Equations, Calculus 1, calculus 2, Numerical Computations(Under Graduate Level)
Publications:
[21] With F. Ghanbari, K. Ghanbari, High order Legendre collocation method for fractional order linear semi explicit differential algebraic equations, Elec. Trans. Numer. Anal.(ETNA), Accepted. [20] With H. Zahed, H. Rezapour, Selffocusing and defocusing of cosh Gaussian laser beam in the presence of nonlinearity of ponderomotive force and temperature gradient, Chinese Journal of Physics, 56(2018), no. 5, 18341844. [19] Discrete collocation method for Volterra type weakly singular integral equations with logarithmic kernels, Iran. J. Numer. Anal. Optim.(IJNAO), 8(2018), no. 2, 95117. [18] With F. Ghanbari, K. Ghanbari, Generalized Jacobi Galerkin method for nonlinear fractional differential algebraic equations, Computational & Applied Mathematics, 37(2018), 54565475. [17] Computational Legendre Tau method for Volterra Hammerstein pantograph integral equations , Bull. Iran. Math. Soc., Accepted. [16] Spectrally accurate and wellposed Jacobi Galerkin method for multiple delays pantograph integral equations, Iran. J. Sci. Technol. Trans. A Sci., Accepted. [15] Numerical analysis of an operational Jacobi Tau method for fractional weakly singular integrodifferential equations, Appl. Numer. Math., (2017), 121(2017), 5267.
[14] Operational MuntzGalerkin approximation fo AbelHammerstein integral equations of the second kind, Elec. Trans. Numer. Anal., 45(2016), 183200. [13] Numerical treatment of a wellposed Chebyshev Tau method for BagleyTorvik equation with highorder of accuracy, Numer. Algorithms, 72(2016), no. 4, 875891 . [12] Discrete Galerkin method for fractional integrodifferential equations, Acta Math. Sci., 2016, 36B(2): 560578. [11] With M. Gholipour, Discrete Galerkin method for higher evenorder integrodifferential equations with varable coefficients. Computational methods for differential equations, 3(2015), no. 1, 3644. [10] With F. Ghoreishi, H. M. Srivastava, The MuntzLegendre Tau method for Fractional Differential equations, Appl. Math. Model., 40(2016), 671684. [9] High order modified Tau method for nonsmooth solutions of Abel integral equations, Elec. Trans. Numer. Anal., 44(2015). 462471. [8] Reconstruction of exponentially rate of convergence to Legendre collocation solution of a class of Fractional IntegroDifferential equations, J. Comput. Appl. Math., 279(2015), 145158. [7] Operational Tau method for nonlinear multiorder FDE's, Iran. J. Numer. Anal. Optim.(IJNAO), 4, No. 2 (2014), 4355. [6] With F. Ghoreishi,Convergence analysis of operational Tau method for Abel type Volterra integral equations, Elec. Trans. Numer. Anal., 41 (2014), 289305.
[5] With F. Ghoreishi, Convergence analysis of spectral Tau method for fractional Riccati differential equations, Bull. Iran. Math. Soc., 40, 5(2014), 12751290.
[4] With F. Ghoreishi, Spectral Collocation Method for multiorder fractional differential equations, Int. J. Comput. Methods, 11, 5 (2014), 1350072(23pp)
[3] With F. Ghoreishi, The L^2convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations, Numer. Algorithms, 58, (2011), 475496.
[2] With S. M. Hosseini, Rescale and Modify implementation of IRKs methods, Numer. Algorithms, 47 (2008), 315325.
[1] With S. M. Hosseini, Some implementation aspects of the general linear methods with inherent RungeKutta stability, Iranian Journal of Mathematical Sciences and Informatics, 3, (2008), 6376.
Presentations:
[10] With F. Ghanbari and K. Ghanbari, The MuntzJacobi collocation method for solving fractional differential algebraic equations, The first international conference on boundary value problems and applications, University of Tabriz, 2018, Iran. [9] With F. Ghanbari and K. Ghanbari, The Legendre collocation method for nonlinear fractional order integrodifferential algebraic equations with smooth solutions, 48th Annual Iranian mathematics conference, University of BuAli sina, 2017, Iran. [8] With F. Ghanbari and K. Ghanbari, The pseudospectral method for solving fractional differential algebraic equations(FDAE), 6th seminar on numerical analysis, university of Maragheh, 2016, Iran.
[7] With S. Kafili, Piecewise collocation method for the numerical solution of fractional integrodifferential equations with weakly singular kernels, 6th seminar on numerical analysis, university of Maragheh, 2016, Iran. [6] With H. Ansari, Discrete Galerkin method for pantograph type Volterra integral equations, 6th seminar on numerical analysis, university of Maragheh, 2016, Iran. [5] With S. M. Hosseini, Basic topics in general linear methods with inherent RungeKutta stability for ODE's, 40th Annual Iranian mathematics conference, Sharif University of Technology, Iran. [4] With F. Ghoreishi, Numerical solution of fractional Integrodifferential equations by Galerkin method with an error estimation, 40th Annual Iranian mathematics conference, Sharif University of Technology, Iran. [3] With F. Ghoreishi, Orthogonal Collocation method for fractional Integrodifferential equations, 41th Annual Iranian mathematics conference, University of Urmia, Iran. [2] With F. Ghoreishi, Condition Number Analysis of the Tau method for FIDE's, 42th Annual Iranian mathematics conference, VlieAsr university of Rafsanjan, Iran. [1] Petrov Galerkin Method for Fredholm Type Fractional IntegroDifferential Equations, 12th Seminar on Differential Equations and Dynamical System, University of Tabriz, Iran. Graduate students:
Ph. D. students: [1] F. Ghanbari, (Joint with Dr. K. Ghanbari), In Progress, [2] Y. Talaei, (Joint with Dr. S. Shahmorad), In Progress, [3] H. Rezapour, (Joint with Dr. H. Zahed), In Progress, [4] A. Faghih, In Progress, M. Sc students: [1] M. Gholipour, Convergence analysis of spectral Galerkin method for numerical solution of highorder differential equations, September 2015. [2] S. Kafili, Piecewise collocation methods for fractional integrodifferential equations with weakly singular kernels, September 2016. [3] H. Ansari, Spectral methods for pantographtype differential and integral equations, September 2016. [4] Z. Keramati, Convergence analysis of spectral and pseudospectral Galerkin methods for Volterra type integral equations, September 2016. [5] N. Ayazi, Fractional SturmLiouville equations and their applications, July 2018. [6] Z. Shahbazi, A multidomain spectral method for fractional differential equations, In Progress. [7] M. Parvizi, Fractional Laguerre polynomials and their applications, In Progress. [8] Sh. Razmavari, Fractional Gauss quadrature and its application in fractional variational problems, In Progress. Reviewer of the journals: Applied Numerical Mathematics, Journal of Computational and Applied Mathematics, Applied Mathematical Modelling, Computational and Applied Mathematics, Mathematical Modelling and Analysis, Applied Mathematics and Computation, Mathscinet, Journal of Mathematical Extension, Iranian Journal of Science and Technology(Scieneces). Awards and achievements:
Memberships:


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