1. J.D.C. Little, Aggregate Advertising Models: The State of the Art, Oper. Res. 27 (1979), 629-667.
2. K.M. Lancaster, A.S. Judith, Computer-Based Advertising Budgeting Practices of Leading U.S. Consumer Advertisers, J Advert. 12 (4) (1983), 4-9.
3. D.M. Hanssens, J.P. Leonard, L. S. Randall, Market Response Models: Econometric and Time Series Analysis, Boston: Kluwer Academic Publishers, 2001.
4. L. Friedman, Game-Theory Models in the Allocation of Advertising Expenditures, Oper. Res. 6 (1958), 699-709.
5. E. Dockner, J. Steffen, V. L. Ngo, S. Gerhard, Differential Games in Economics and anagement Science, Cambridge: Cambridge University Press, 2000.
6. K.M. Ramachandran, C.P. Tsokos, Stochastic differential games: theory and applications, Atlantis Press, USA, 2012.
7. M. Jensen, I. Smears, On the convergence of the finite element methods for Hamilton Jacobi Bellman equations, SIAM J. Numer. Anal. 51 (2013), 137–162.
8. F. Camilli and E.R. Jakobsen, A finite element like scheme for integro-partial differential Hamilton-Jacobi-Bellman equations, SIAM J. Numer. Anal. 47 (2009), 2407–2431.
9. H. Dong, N.V. Krylov, The rate of convergence of finite-difference approximations for parabolic Bellman equations with Lipschitz coefficients in cylindrical domains, Appl. Math. Optim. 56 (2007), 37–66.
10. N.V. Krylov, On the rate of convergence of finite-difference approximations for Bellman’s equation, St. Petersburg Math. J. 9(3) (1997), 245–256.
11. N.V. Krylov, On the rate of convergence of finite-difference approximations for Bellman’s equations with variable coefficients, Probab. Theory Related Fields 117(1) (2000), 1–16.
12. N.V. Krylov, The rate of convergence of finite-difference approximations for Bellman equations with Lipschitz coefficients, Appl. Math. Optim. 52(3) (2005), 365–399.
13. H. Dong and N.V. Krylov, On the rate of convergence of finite-difference approximations for Bellman’s equation with constant coefficients, Algebra Anal. 17 (2006), 295–313.
14. B. Fornberg, A practical guide to pseudospectral methods, Cambridge Monographs, 1995.
15. C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamics, Springer, NewYork, 1988.
16. J. Boyd, Chebyshev and Fourier Spectral Methods, Dover, second edition, 2001.
17. J.C. Mason, D.C. Handscomb, Chebyshev Polynomials, CRC Press LLC, 2003.
18. Z. Avazzadeh, M. Heydari, Chebyshev polynomials for solving two dimensional linear and nonlinear integral equations of the second kind, Comput. Appl. Math. 31 (2012), 127-142.
19. E. Scheiber, On the Chebyshev approximation of a function with two variables, arXiv:1504.04693, 2015.
20. E. Tohidi, Application of Chebyshev collocation method for solving two classes of non-classical parabolic PDEs, Ain Shams Eng. J. (2015), 373-379.
21. V. S. Chelyshkov, Alternative Orthogonal Polynomials and quadratures, ETNA, Electron. Trans. Numer. Anal. 25 (2006), 17-26.
22. L. Moradi, F. Mohammadi, D. Baleanu, A direct numerical solution of time-delay fractional optimal control problems by using Chelyshkov wavelets, J. Vib. Control. 25 (2018), 310-324.
23. C. Oğuz, M. Sezer, A.D. Oguz, Chelyshkov collocation approach to solve the systems of linear functional differential equations, New Trends Math. Sci. 4 (2015), 83-97.
24. C. Oğuz, M. Sezer, Chelyshkov collocation method for a class of mixed functional integro-differential equations, Appl. Math. Comput. 259 (2015), 943-954.
25. Y. Talaei, M. Asgari, An operational matrix based on Chelyshkov polynomials for solving multi-order fractional differential equations, Neural. Comput. Appl. 30 (2018), 1369-1378.
26. P. Rahimkhani, Y. Ordokhani, Numerical Solution of Volterra–Hammerstein Delay Integral Equations, Iran. J. Sci. Technol. Trans. A Sci. 44 (2020), 445-457.
27. D. S. Mohamed, Chelyshkov’s Collocation Method for Solving Three-Dimensional Linear Fredholm Integral Equations, MathLAB Journal 4 (2019), 163-171.
28. K. G. Vamvoudakis, F.L. Lewis, Multi-player non-zero-sum games: online adaptive learning solution of coupled Hamilton-Jacobi equations, Automatica 47(8) (2011), 1556-1569.
29. D. Vrabie, F. L. Lewis, Integral reinforcement learning for online computation of feedback Nash strategies of nonzero-sum differential games, Proceedings of the IEEE conference on Decis. Control. (2010), 3066-3071.
30. D. Liu, Q. Wei, D. Wang, X. Yang, H. Li, Adaptive Dynamic Programming with Applications in Optimal Control, Adv. Ind. Control. springer, 2017.
31. H. Li, D. Liu, D. Wang, Adaptive dynamic programming for solving nonzero-sum differential games, Conf. Intell. Control and Autom. Sci. (2013), 587-591.
32. E. Suli and D. F. Mayers, An Introduction to Numerical Analysis, Cambridge University press, 2003.
33. M. Gasca, T. Sauer, On the history of multivariate polynomial interpolation, J. Comput. Appl. Math. 122 (2000), 23-35.
34. Z. Nikooeinejad, A. Delavarkhalafi, M. Heydari, A numerical solution of open-loop Nash equilibrium in nonlinear differential games based on Chebyshev pseudospectral method, J. Comput. Appl. Math. 300 (2016), 369-384.
35. Z. Nikooeinejad, A. Delavarkhalafi, M. Heydari, Application of shifted Jacobi pseudospectral method for solving (in)finite-horizon minimax optimal control problems with uncertainty, Internat. J. Control. 13 (2017), 725-739.
36. Z. Nikooeinejad, M. Heydari, Nash equilibrium approximation of some class of stochastic differential games: A combined Chebyshev spectral collocation method with policy iteration, J. Comput. Appl. Math. 362 (2019), 41-54.
37. M. Saffarzade, G. B. Loghmani, M. Heydari, An iterative technique for the numerical solution of nonlinear stochastic It -Volterra integral equations, J. Comput. Appl. Math. 333 (2018), 74-86.
38. S. Alipour, F. Mirzaee, An iterative algorithm for solving two dimensional nonlinear stochastic integral equations: A combined successive approximations method with bilinear spline interpolation, Appl. Math. Comput. 371 (2020), 124947.
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