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Nemati, Mehran, Shafiee, Mahmoud, Ebrahimi, Hamideh. (1401). A meshless technique based on the radial basis functions for solving systems of partial differential equations. سامانه مدیریت نشریات علمی, 10(2), 526-537. doi: 10.22034/cmde.2021.39707.1740
Mehran Nemati; Mahmoud Shafiee; Hamideh Ebrahimi. "A meshless technique based on the radial basis functions for solving systems of partial differential equations". سامانه مدیریت نشریات علمی, 10, 2, 1401, 526-537. doi: 10.22034/cmde.2021.39707.1740
Nemati, Mehran, Shafiee, Mahmoud, Ebrahimi, Hamideh. (1401). 'A meshless technique based on the radial basis functions for solving systems of partial differential equations', سامانه مدیریت نشریات علمی, 10(2), pp. 526-537. doi: 10.22034/cmde.2021.39707.1740
Nemati, Mehran, Shafiee, Mahmoud, Ebrahimi, Hamideh. A meshless technique based on the radial basis functions for solving systems of partial differential equations. سامانه مدیریت نشریات علمی, 1401; 10(2): 526-537. doi: 10.22034/cmde.2021.39707.1740

A meshless technique based on the radial basis functions for solving systems of partial differential equations

Computational Methods for Differential Equations
مقاله 18، دوره 10، شماره 2، تیر 2022، صفحه 526-537    اصل مقاله (299.63 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.39707.1740
نویسندگان
Mehran Nemati؛ Mahmoud Shafiee* ؛ Hamideh Ebrahimi
Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran.
چکیده
The radial basis functions (RBFs) methods were first developed by Kansa to approximate partial differential equations (PDEs). The RBFs method is being truly meshfree becomes quite appealing, owing to the presence of distance function, straight-forward implementation, and ease of programming in higher dimensions. Another considerable advantage is the presence of a tunable free shape parameter, contained in most of the RBFs that control the accuracy of the RBFs method. Here, the solution of the two-dimensional system of nonlinear partial differential equations is examined numerically by a Global Radial Basis Functions Collocation Method (GRBFCM). It can work on a set of random or uniform nodes with no need for element connectivity of input data. For the timedependent partial differential equations, a system of ordinary differential equations (ODEs) is derived from this scheme. Like some other numerical methods, a comparison between numerical results with analytical solutions is implemented confirming the efficiency, accuracy, and simple performance of the suggested method.
کلیدواژه‌ها
Global meshless method؛ Radial basis functions؛ Method of lines؛ Partial differential equations
مراجع
  • [1]          M. Abbaszadeh and M. Dehghan, Meshless upwind local radial basis function-finite difference technique to simulate the time-fractional distributed-order advection–diffusion equation, Engineering with computers, (2019), 1–17.
  • [2]          M. Abbaszadeh and M. Dehghan, Reduced order modeling of time-dependent incompressible Navier–Stokes equa- tion with variable density based on a local radial basis functions-finite difference (LRBF-FD) technique and the POD/DEIM method, Computer Methods in Applied Mechanics and Engineering, 364 (2020), 112914.
  • [3]          M. Abbaszadeh and M. Dehghan, An upwind local radial basis functions-differential quadrature (RBFs-DQ) technique to simulate some models arising in water sciences, Ocean Engineering, 197 (2020), 106844.
  • [4]          M. Abbaszadeh and M. Dehghan, Simulation flows with multiple phases and components via the radial basis functions-finite difference (RBF-FD) procedure: Shan-Chen model, Engineering Analysis with Boundary Elements, 119 (2020), 151–161.
  • [5]          A. Ali and S. Haq, A computational meshfree technique for the numerical solution of the two-dimensional coupled Burgers’ equations, International Journal for Computational Methods in Engineering Science and Mechanics, 10(5) (2009), 406–422.
  • [6]          S. Arbabi, A. Nazari, and M. T. Darvishi, A two-dimensional Haar wavelets method for solving systems of PDEs, Applied Mathematics and Computation, 292 (2017), 33–46.
  • [7]          S. N. Atluri and S. Shen, The Meshless  Local  Petrov-Galerkin  (MLPG)  method:  A  simple & less-costly  alternative  to the finite element and boundary element methods, Computer Modeling in Engineering and Sciences,  3  (1) (2002), 11–51.
  • [8]          T. Belytschko, et al, Meshless methods: an overview and recent developments, Computer methods in applied mechanics and engineering, 139(1-4) (1996), 3–47.
  • [9]          J. Biazar and M. Eslami, A new homotopy perturbation method for solving systems of partial differential equations, Computers & Mathematics with Applications, 62(1) (2011), 225–234.
  • [10]        M. D. Buhmann, Radial basis functions: theory and implementations, Cambridge university press, 2003.
  • [11]        C. K. Chen and S. H. Ho, Solving partial differential equations by two-dimensional differential transform method, Applied Mathematics and computation, 106(2-3) (1999), 171–179.
  • [12]        Y. Cherruault and G. Adomian, Decomposition methods: a new proof of convergence, Mathematical and Computer Modelling, 18(12) (1993), 103–106.
  • [13]        Y. Dereli and R. Schaback, The meshless kernel-based method of lines for solving the equal width equation, Applied Mathematics and Computation, 219(10) (2013), 5224–5232.
  • [14]        G. E. Fasshauer, Solving partial differential equations by collocation with radial basis functions, Proceedings of Chamonix 1997, (1996), 1–8.
  • [15]        M. A. Golberg, C. S. Chen, and S. R. Karur, Improved multiquadric approximation for partial differential equations, Engineering Analysis with boundary elements 18(1) (1996), 9–17.
  • [16]        R. L. Hardy, Multiquadric equations of topography and other irregular surfaces, Journal of geophysical research, 76(8) (1971), 1905–1915.
  • [17]        J. H. He, Variational iteration method–a kind of non-linear analytical technique: some  examples,  International  journal of non-linear mechanics, 34(4) (1999), 699–708.
  • [18]        J. H. He, Homotopy perturbation technique, Computer methods in applied mechanics and engineering, 178(3-4) (1999), 257–262.
  • [19]        J. H. He, A coupling method of a homotopy technique and perturbation technique for non-linear problems , International journal of non-linear meachanics, 35(1) (2000), 37–43.
  • [20]        C. Franke and R. Schaback, Convergence order estimates of meshless collocation methods  using  radial  basis  functions, Advances in computational mathematics, 8(4) (1998), 381–399.
  • [21]        C-S. Huang, C-F. Lee, and AH-D. Cheng, Error  estimate,  optimal  shape  factor,  and  high  precision  computation    of multiquadric collocation method, Engineering Analysis with Boundary Elements, 31(7) (2007), 614–623.
  • [22]        C. Franke and R. Schaback, Solving partial diffrential equations by collocation using radial basis functions, Applied Mathematics and computation, 93(1) (1998), 73–82.
  • [23]        E. J. Kansa, Application of Hardy’s multiquadric interpolation to hydrodynamics, (1986), 111–116.
  • [24]        E. J. Kansa, Multiquadrics -A scattered data approximation scheme with applications to computational - I surface approximations and partial derivative estimates, Computers & Mathematics with applications, 19(8-9) (1990), 127–145.
  • [25]        W. R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions. II, Mathematics of Computation, 54(189) (1990), 211-230.
  • [26]        M. Matinfar, M. Saeidy, and B. Gharahsuflu, A new homotopy analysis method for finding the exact solution of systems of partial differential equations,Selcuk university Research center of Applied Mathematics, 2012.
  • [27]        C. A. Micchelli, Interpolation of scattered data: distance matrices and conditionally positive definite functions, Constructive approximation, 2(1) (1986), 11–22.
  • [28]        M. Mohammadi, F. S. Zafarghandi, E. Babolian, and S. Jvadi, A local reproducing kernel method accompanied by some different edge improvement techniques: application to the Burgers’ equation, Iranian Journal of Science and Technology, Transactions A: Science, 42(2) (2018), 857–871.
  • [29]        S. Müller and R. Schaback, A Newton basis for kernel spaces,Journal of Approximatin theory, 161(2) (2009), 645–655.
  • [30]        M. L. Overton, Numerical computing with IEEE floating point arithmetic, Society for Industrial and Applied Mathematics, 2001.
  • [31]        S. A. Sarra, A local radial basis function method for advection–diffusion–reaction equations on complexly shaped domains, Applied mathematics and Computation, 218(19) (2012), 9853–9865.
  • [32]        R. Schaback, Error estimates and condition numbers for radial basis function interpolation, Advances in Compu- tational Mathematics, 3(3) (1995), 251–264.
  • [33]        R. Schaback, A computational tool for comparing all linear PDE solvers, Advances in Computational Mathematics, 41(2) (2015), 333–355.
  • [34]        A. M. Wazwaz, The decomposition method applied to systems of partial differential equations and to the reaction– diffusion Brusselator model, Applied mathematics and computation, 110(2-3) (2000), 251–264.
  • [35]        F. S. Zafarghandi , et al, A localized Newton basis functions meshless method for the numerical solution of the nonlinear coupled Burgers’ equations, International Journal of Numerical Methods for Heat & Fluid Flow, 2017.
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