دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,365
تعداد مقالات16,812
تعداد مشاهده مقاله54,155,467
تعداد دریافت فایل اصل مقاله16,866,661
Golbabai, Ahmad, Safaei, Nima, Molavi-Arabshahi, Mahboubeh. (1401). Numerical solution of optimal control problem for economic growth model using RBF collocation method. سامانه مدیریت نشریات علمی, 10(2), 327-337. doi: 10.22034/cmde.2021.40223.1757
Ahmad Golbabai; Nima Safaei; Mahboubeh Molavi-Arabshahi. "Numerical solution of optimal control problem for economic growth model using RBF collocation method". سامانه مدیریت نشریات علمی, 10, 2, 1401, 327-337. doi: 10.22034/cmde.2021.40223.1757
Golbabai, Ahmad, Safaei, Nima, Molavi-Arabshahi, Mahboubeh. (1401). 'Numerical solution of optimal control problem for economic growth model using RBF collocation method', سامانه مدیریت نشریات علمی, 10(2), pp. 327-337. doi: 10.22034/cmde.2021.40223.1757
Golbabai, Ahmad, Safaei, Nima, Molavi-Arabshahi, Mahboubeh. Numerical solution of optimal control problem for economic growth model using RBF collocation method. سامانه مدیریت نشریات علمی, 1401; 10(2): 327-337. doi: 10.22034/cmde.2021.40223.1757

Numerical solution of optimal control problem for economic growth model using RBF collocation method

Computational Methods for Differential Equations
مقاله 4، دوره 10، شماره 2، تیر 2022، صفحه 327-337    اصل مقاله (155.89 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.40223.1757
نویسندگان
Ahmad Golbabai؛ Nima Safaei؛ Mahboubeh Molavi-Arabshahi*
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
چکیده
In the current paper, for the economic growth model, an efficient numerical approach on arbitrary collocation points is described according to Radial Basis Functions (RBFs) interpolation to approximate the solutions of optimal control problems. The proposed method is based on parametrizing the solutions with any arbitrary global RBF and transforming the optimal control problem into a constrained optimization problem using arbitrary collocation points. The superiority of the method is its flexibility to select between different RBF functions for the interpolation and also parametrization an extensive range of arbitrary nodes. The Lagrange multipliers method is employed to convert the constrained optimization problem into a system of algebraic equations. Numerical results approve the accuracy and performance of the presented method for solving optimal control problems in the economic growth model. 
کلیدواژه‌ها
Optimal control problem؛ Economic growth model؛ RBF collocation method؛ Lagrange multipliers
مراجع
  • [1]          M. D. Buhmann, Radial Basis Functions: Theory and Implementation, Cambridge: Cambridge University Press, 2004.
  • [2]          D. N. Burghes and A. Graham, Control and Optimal Control Theories with Applications, Horwood Publishing Limited, 2004.
  • [3]          S. Effati and M. Pakdaman, Optimal control problem via neural networks, Neural Computing and Applications, 23(7) (2013), 2093-2100.
  • [4]          G. Fasshuar, Meshfree approximation methods with MATLAB, World Scientific publishing, 2017.
  • [5]          A. Golbabai and E. Mohebianfar, A new method for evaluating options based on multiquadric RBF-FD method, Applied Mathematics and Computation, 308 (2017), 130-141.
  • [6]          A. Golbabai, E. Mohebianfar, and H. Rabiei, On the new variable shape parameter strategies for radial basis  functions, Computational and Applied Mathematics, 34 (2015), 691-704.
  • [7]          A. Golbabai and A. Saeedi, An Improved RBF Method for Solving Variational Problems Arising from Dynamic Economic Models, Computational Economics, 46(2) (2015), 275-285.
  • [8]          V. Grygorkiv and O. Vinnychuk, Dynamics and optimal control investments in the economic growth model with condition of ecological balance, Intellectual Economics, 8(2) (2014), 23-33.
  • [9]          R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, Journal of Geophysical Research, 76(8) (1971), 1905-1915.
  • [10]        E. J. Kansa, Multiquadrics-A scattered data approximation scheme with applications to computational  fluid-  dynamics-I surface approximations and partial derivative estimates, Computers & Mathematics with Applications, 19(8) (1990), 127-145.
  • [11]        C. A. Micchelli, Interpolation of scattered data: distance matrices and conditionally positive definite functions, Constructive Approximation, 2(1) (1986), 11-22.
  • [12]        H. Mirinejad and T. Inanc, An RBF collocation method for solving optimal control problems,Robotics and Au- tonomous Systems, 87 (2017), 219-225.
  • [13]        A. Novales, E. Fernandez, and J. Ruiz, Economic Growth: Theory and Numerical Solution Methods, Springer Verlag Berlin Heidelberg, 2009.
  • [14]        M. Pakdaman and Sohrab Effati, Approximating the Solution of Optimal Control Problems by Fuzzy Systems, Neural Processing Letters, 43 (2016), 667-686.
  • [15]        J. A. Rad, S. Kazem,and K. Parand, Radial basis functions approach on optimal control problems: a numerical investigation, Journal of Vibration and Control, 20(9) (2014), 1394-1416.
  • [16]        R. Schaback, Improved error bounds for scattered data interpolation by radial basis functions, Mathematics of Computation, 68(225) (1999), 201-206.
  • [17]        R. M. Solow, A Contribution to the Theory of Economic Growth, The Quarterly Journal of Economics, 70(1) (1956), 65-94.
  • [18]        H. Wendland, Scattered Data Approximation, Cambridge: Cambridge University Press, 2005.
آمار
تعداد مشاهده مقاله: 931
تعداد دریافت فایل اصل مقاله: 932


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب