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

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Niknam, Sepideh, Adibi, Hojatollah. (1401). A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions. سامانه مدیریت نشریات علمی, 10(4), 969-985. doi: 10.22034/cmde.2021.42440.1829
Sepideh Niknam; Hojatollah Adibi. "A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions". سامانه مدیریت نشریات علمی, 10, 4, 1401, 969-985. doi: 10.22034/cmde.2021.42440.1829
Niknam, Sepideh, Adibi, Hojatollah. (1401). 'A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions', سامانه مدیریت نشریات علمی, 10(4), pp. 969-985. doi: 10.22034/cmde.2021.42440.1829
Niknam, Sepideh, Adibi, Hojatollah. A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions. سامانه مدیریت نشریات علمی, 1401; 10(4): 969-985. doi: 10.22034/cmde.2021.42440.1829

A numerical solution of two-dimensional hyperbolic telegraph equation based on moving least square meshless method and radial basis functions

Computational Methods for Differential Equations
مقاله 10، دوره 10، شماره 4، دی 2022، صفحه 969-985    اصل مقاله (1.12 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.42440.1829
نویسندگان
Sepideh Niknam؛ Hojatollah Adibi*
Department of Applied Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
چکیده
In this research, a linear combination of moving least square (MLS) and local radial basis functions (LRBFs) is considered within the framework of the meshless method to solve the two-dimensional hyperbolic telegraph equation. Besides, the differential quadrature method (DQM) is employed to discretize temporal derivatives. Furthermore, a control parameter is introduced and optimized to achieve minimum errors via an experimental approach. Illustrative examples are provided to demonstrate the applicability and efficiency of the method. The results prove the superiority of this method over using MLS and LRBF individually. 
کلیدواژه‌ها
Meshless method؛ Moving least square؛ Local radial basis function؛ Two-dimensional hyperbolic telegraph equation؛ Differential quadrature method
مراجع
  • [1]          C. A. Brebbia , J. C. F. Teles, and L.C. Wrobel, Boundary element techniques, Berlin: Springer, 1984.
  • [2]          M. Dehghan and A. Shokri, A Meshless Method for Numerical Solution of a Linear Hyperbolic Equation with Variable Coefficients in Two Space Dimensions, Numer. Methods Partial Differential Eq., 25 (2009), 494-506.
  • [3]          M. Dehghan and A. Ghesmati, Combination of meshless local weak and strong (MLWS) forms to solve the two dimensional hyperbolic telegraph equation, Engineering Analysis with Boundary Elements, 34 (2010), 324-336.
  • [4]          M. Dehghan and A. Shokri, A numerical method for solving the hyperbolic telegraph equation, Numerical Methods Partial Differential Eq, 24 (2008), 1080-1093.
  • [5]          M. Dehghan and R. Salehi, A method based on meshless approach for the numerical solution of the two-space dimensional hyper bolic telegraph equation, Math. Meth. Appl. Sci.
  • [6]          F. Gao and C. Chi, Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equa- tion, Appl. Math. Comput, 187 (2007), 1272-1276.
  • [7]          R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, Journal of Geophysical Research, 76(8) (1971), 1905-1915.
  • [8]          R. Jiwari, S. Pandit, and R. C. Mittal,  A  differential  quadrature  algorithm  to  solve  the  two  dimensional  lin-  ear hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions, Applied Mathematics and Computation, 218 (2012), 7279-7294.
  • [9]          S. Kazem, J. A. Rad, and K. Parand, A meshless method on non-Fickian flows with mixing length growth in porous media based on radial basis functions: a comparative study, Comput. Math. Appl, 64 (2012), 399-412.
  • [10]        D. Levin, The approximation power of moving least-squares, Math. Comput, 67 (1998), 1517-1531.
  • [11]        K. M. Liew, C. Yumin, and S. Kitipornchai, Boundary Element-free method (BEFM) for two-dimensional elasto- dynamic analysis using Laplace transforms, Int. J. Numer. Methods. Eng, 64(12) (2005), 1610-1627.
  • [12]        G. R. Liu, Moving Beyond the Finite Element Method, Second Edition, Boca Raton, CRC Press, 2009.
  • [13]        C. Micchelli, Interpolation of scattered data: Distance matrices and conditionally positive definite functions, Constructive Approximation, 2 (1986), 11-22.
  • [14]        S. Patankar, Numerical heat transfer and fluid flow, USA, Taylor & Francis, 1980.
  • [15]        B. Rezapour and M. A. Fariborzi Araghi, Nanoparticle delivery through single walled carbon  nanotube subjected   to various boundary conditions, Microsyst. Technol, 25 (2019), 1345-1356.
  • [16]        D. Rostamy, M. Emamjomea, and S. Abbasbandy, A meshless technique based on the pseudospectral radial basis  functions method for solving the two-dimensional hyperbolic telegraph equation, Phys. J. Plus, (2017), 132-263.
  • [17]        K. Salkauskas, Moving least squares interpolation with thin-plate splines and radial basis functions,  Comput.  Math. Appl, 24 (1992), 177-185.
  • [18]        S. A. Sarra, A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs, Numerical Method Partial Differential Equations, 24(2) (2008), 670-686.
  • [19]        A. Shokri and M. Dehghan, Meshless method using radial basis functions for the numerical solution of two- dimensional complex Ginzburg–Landau equation, Comput. Model Eng. Sci, 34 (2012), 333-358.
  • [20]        A. Shokri and M. Dehghan, A Not-a-Knot meshless method using radial basis functions and predictor–corrector scheme to the numerical solution of improved Boussinesq equation, Comput. Phys. Commun, 181 (2010), 1990- 2000.
  • [21]        C. Shu and K. S. Yao, Block-marching in time with DQ discretization: an efficient method for time-dependent problems, Comput. Methods Appl. Mech. Eng, 191 (2002), 4587-4597.
  • [22]        G. D. Smith, Numerical solution of partial differential equations: finite difference methods, USA, Oxford University Press, 1986.
  • [23]        M. Tatari and M. Dehghan, A method for solving partial differential equations via radial basis functions: appli- cation to the heat equation, Eng. Anal. Bound. Elem, 34 (2010), 206-212.
  • [24]        B. Wang, A local meshless method based on moving least squares and local radial basis functions, Engineering Analysis with Boundary Elements, 50 (2015), 395-401.
  • [25]        Z. Zhang, L. Yumin, K. M. Cheng, and Y. Y. Lee, Analyzing 2D fracture problems with the improved element-free Galerkin method, Eng. Anal. Boundary Elem, 32 (2008), 241-250.
  • [26]        Z. Zhang, P Zhao, and K. M. Liew, Improved element-free Galerkin method for two- dimensional potential problems, Eng. Anal. Boundary Elem, 33 (2009), 547-554.
  • [27]        O. C. Zienkiewicz and R. L. Taylor, The finite element method, Bristol, Butterworth, 2000.
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