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

 آمار

تعداد نشریات45
تعداد شماره‌ها1,530
تعداد مقالات18,634
تعداد مشاهده مقاله61,229,735
تعداد دریافت فایل اصل مقاله22,019,812
Torabi Giklou, Asadollah, Ranjbar, Mojtaba, Shafiee, Mahmoud, Roomi, Vahid. (1400). Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations. سامانه مدیریت نشریات علمی, 10(1), 144-157. doi: 10.22034/cmde.2021.44736.1890
Asadollah Torabi Giklou; Mojtaba Ranjbar; Mahmoud Shafiee; Vahid Roomi. "Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations". سامانه مدیریت نشریات علمی, 10, 1, 1400, 144-157. doi: 10.22034/cmde.2021.44736.1890
Torabi Giklou, Asadollah, Ranjbar, Mojtaba, Shafiee, Mahmoud, Roomi, Vahid. (1400). 'Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations', سامانه مدیریت نشریات علمی, 10(1), pp. 144-157. doi: 10.22034/cmde.2021.44736.1890
Torabi Giklou, Asadollah, Ranjbar, Mojtaba, Shafiee, Mahmoud, Roomi, Vahid. Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations. سامانه مدیریت نشریات علمی, 1400; 10(1): 144-157. doi: 10.22034/cmde.2021.44736.1890

Collocation method based on radial basis functions via symmetric variable shape parameter for solving a particular class of delay differential equations

Computational Methods for Differential Equations
مقاله 10، دوره 10، شماره 1، فروردین 2022، صفحه 144-157    اصل مقاله (371.27 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.44736.1890
نویسندگان
Asadollah Torabi Giklou1، 2؛ Mojtaba Ranjbar* 3، 4؛ Mahmoud Shafiee2؛ Vahid Roomi3
1Department of Mathematics, Guilan Science and Research Branch, Islamic Azad University, Rasht, Iran.
2Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
3Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
4Faculty of Financial Sciences, Kharazmi University, Tehran, Iran.
چکیده
In this article, we use the collocation method based on the radial basis functions with symmetric variable shape parameter (SVSP) to obtain numerical solutions of neutral-type functional-differential equations with proportional delays. In this method, we control the absolute errors and the condition number of the system matrix through the program prepared with Maple 18.0 by increasing the number of collocation points that have a direct effect on the defined shape parameter. Also, we present the tables of the rate of the convergence (ROC) to investigate and show the convergence rate of this method compared to the RBF method with constant shape parameter. Several examples are given to illustrate the efficiency and accuracy of the introduced method in comparison with the same method with the constant shape parameter (CSP) as well as other analytical and numerical methods. Comparison of the obtained numerical results shows the considerable superiority of the collocation method based on RBFs with SVSP in accuracy and convergence over the collocation method based on the RBFs with CSP and other analytical and numerical methods for delay differential equations (DDEs).
کلیدواژه‌ها
Functional-differential equation؛ Proportional delay؛ Radial basis function؛ Variable shape parameter
مراجع
  • [1]          H. Adibi and J. Es’haghi, Numerical solution for biharmonic equation using multilevel radial basis functions and domain decomposition methods. Appl. Math. Comput., 186 (2007), 246–255.
  • [2]          M. D. Buhmann, Radial basis functions, Acta Numerica, 9 (2000), 1-38.
  • [3]          M. Chamek, T. M. Elzaki and N. Brik, Semi-analytical solution for some proportional delay differential equations,   SN Applied Sciences, 148(1) (2019), DOI: 10.1007/s42452-018-0130-8.
  • [4]          X. Chen and L. Wang, The variational iteration method for solving a neutral functionaldifferential equation with proportional delays, Computers and Mathematics with Applications, 59 (2010), 26962702.
  • [5]          S. Davaeifar and J. Rashidinia, Solution of a system of delay differential equations of multi pantograph type, Journal of Taibah University for Science, 11 (2017), 11411157.
  • [6]          M. Dehghan and A. Shokri, Numerical solution of the nonlinear Klein–Gordon equation using radial basis func- tions, J. Comput. Appl. Math., 230(2) (2009), 400–410.
  • [7]          M. Dehghan and M. Tatari, Determination of a control parameter in a one-dimentional parabolic equation using the method of radial basis functions, Math. Comp. Modeling, 44 (2006), 1160-1168.
  • [8]          O. Farkhondeh Rouz, Preserving asymptotic mean-square stability of stochastic theta scheme for systems of sto-  chastic delay differential equations, Computational Methods for Differential Equations, 8(3) (2020), 468-479.
  • [9]          R. Franke, Scattered data interpolation: tests of some methods, Math. Comput., 38 (1982), 181-200.
  • [10]        F. Ghomanjani and M. H. Farahi, The Bezier Control Points Method for Solving Delay Differential Equation, Intelligent Control and Automation, 3 (2012), 188-196.
  • [11]        A. Golbabai, M. Mammadova, and S. Seifollahi, Solving a system of nonlinear integral equations by  an  RBF network, Comput. Math. Appl., 57 (2009), 1651–1658.
  • [12]        A. Golbabai and H. Rabiei, Hybrid shape parameter strategy for the RBF approximation of vibrating systems, International Journal of Computer Mathematics, 89(17) (2012), 2410-2427.
  • [13]        S. Gumgum, N. B. Savasanerial, O. K. Kurkcu, and M. Sezer, Lucas polynomial solution for neutral differential equations with proportional delays, TWMS Journal of Applied and Engineering Mathematics, 10(1) (2020), 259- 269.
  • [14]        R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. Geophy. Res., 76 (1971), 1905- 1915.
  • [15]        A. Isah and C. Phang, Operational matrix based on Genocchi polynomials for solution of delay differential equa- tions, Ain Shams Engineering Journal, 9(4) (2018), 2123-2128.
  • [16]        E. Ishiwata and Y. Muroya, Rational approximation method for delay differential equations with proportional delay, Appl. Math. Comput., 187(2) (2007), 741-747.
  • [17]        E. Ishiwata, Y. Muroya, and H. Brunner, A super-attainable order in collocation methods for differential equations with proportional delay, Appl. Math. Comput., 198(1) (2008), 227-236.
  • [18]        E. J. Kansa, Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynam- ics I: surface approximations and partial derivative estimates, Computers and Mathematics with Applications, 19 (1990), 127145.
  • [19]        E. J. Kansa, Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynam- ics II: solutions to parabolic, hyperbolic, and elliptic partial differential equations, Computers and Mathematics with Applications, 19 (1990), 147161.
  • [20]        E. J. Kansa and R. E. Carlson, Improved accuracy of multiquadric interpolation using variable shape parameters, Comput. Math. Appl., 24 (1992), 99-120.
  • [21]        E. J. Kansa and Y. C. Hon, Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations, Comput. Math. Appl., 39 (2000), 123-137.
  • [22]        A. J. Khattak, S. I. A. Tirmizi, and S. U. Islam, Application of meshfree collocation method to a class of nonlinear partial differential equations, Eng. Anal. Bound. Elem., 33 (2009), 661–667.
  • [23]        L. Khodayari and M. Ranjbar, A Numerical Study of RBFs-DQ Method for Multi-Asset Option Pricing Problems, Bol. Soc. Paran. Mat., 36(1) (2018), 9–23.
  • [24]        O. K. Kurkcu, E. Aslan, and M. Sezer, A novel hybrid method for solving combined functional neutral differential equations with several delays and investigation of convergence  rate  via residual function. Computational Methods   for Differential Equations, 7(3) (2019), 396-417.
  • [25]        N. Mai-Duy, Solving high order ordinary differential equations with radial basis function networks, Int. J. Numer. Meth. Eng., 62 (2005), 824–852.
  • [26]        M. Nouri M, Solving Ito integral equations with time delay via basis functions, Computational Methods for Differential Equations, 8(2) (2020), 268-281.
  • [27]        K. Parand, S. Abbasbandy, S. Kazem, and A. Rezaei, Comparison between two common collocation  approaches  based on radial basis functions for the case  of heat transfer equations arising in porous medium. Commun. Non- linear Sci. Numer. Simul., 16 (2011), 1396–1407.
  • [28]        M. Ranjbar, H. Adibi and M. Lakestani, Numerical solution of homogeneous Smoluchowski’s coagulation equation, Int. J. Comput. Math., 87(9) (2010) 2113–2122.
  • [29]        M. Ranjbar, A new variable shape parameter strategy for Gaussian radial basis function approximation methods, Annals of the University of Craiova, Mathematics and Computer Science Series, 42(2) (2015), 260-272.
  • [30]        J. Rashidinia and M. Khasi, Stable Gaussian radial basis function method for solving Helmholtz equations, Com- putational Methods for Differential Equations, 7(1) (2019), 138-151.
  • [31]        U. K. Sami and A. Ishtiaq, Application of Legendre spectral-collocation method to delay differential and stochastic delay differential equation, AIP ADVANCES 8, 035301 (2018), Doi: 10.1063/1.5016680.
  • [32]        S. A. Sarra and D. Sturgill, A random variable shape parameter strategy for radial basis function approximation methods, Engineering Analysis with Boundary Elements, 33 (2009), 1239-1245.
  • [33]        A.   Torabi   Giklou,    M.   Ranjbar,   M.   Shaffee,    and   V.   Roomi,    VIM-Pad´e   technique   for   solving   nonlin- ear and delay initial value problems, Computational Methods for Differential Equations, (2020), Doi: 10.22034/cmde.2020.35417.1606.
  • [34]        W. Wang and S. Li, On the one-leg θ-methods for solving nonlinear neutral functional differential equations, Appl. Math. Comput., 193(1) (2007), 285-301.
  • [35]        W. Wang, Y. Zhang, and S. Li, Stability of continuous Runge-Kutta-type methods for nonlinear neutral delay- differential equations, Appl. Math. Modell., 33(8) (2009), 3319-3329.
  • [36]        S. Xiang, K. M. Wang, Y. T. Ai, Yun-dong Sha, and H. Shi, Trigonometric variable shape parameter and exponent strategy for generalized multiquadric radial basis function approximation, Applied Mathematical Modelling, 36 (2012), 1931-1938.
  • [37]        L. Xueqin and G. Yue, The RKHSM for solving neutral functional-differential equations with proportional delays, Math. Meth. Appl. Sci., 36 (2013), 642649.
  • [38]        S. Yalcinbas, M. Aynigul, and M. Sezer, A collocation method using Hermite polynomials for approximate solution of pantograph equations, Journal of the Franklin Institute, 348(6) (2011) 1128-1139.
  • [39]        S. Yuzbasi and M. Karacayir, A Galerkin-Like Approach to Solve Multi-Pantograph Type Delay Differential Equa- tions, FILOMAT, 32 (2018), 409-422.
  • [40]        S. Yuzbasi, N. Sahin, and M.Sezer, A Bessel Polynomial Approach For Solving Linear Neutral Delay Differential Equations With Variable Coefficients, Journal Advanced Research in Differential Equations, 3 (2011), 81-101.
  • [41]        S. Yuzbasi, N. Sahin, and M. Sezer, Bessel Collocation Method For Numerical Solution Of Generalized Pantograph Equations, Numerical Methods for Pratial Differential Equations, 28 (2012), 1105-1123.
  • [42]        S. Yuzbasi and M. Sezer, An exponential approximation for solutions of generalized pantograph-delay differential equations, Applied Mathematical Modelling, 37(22) (2013), 9160-9173.
آمار
تعداد مشاهده مقاله: 1,015
تعداد دریافت فایل اصل مقاله: 1,043


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب