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All issues Volume 27 / No 4 (August 2022) Wuhan Univ. J. Nat. Sci., 27 4 (2022) 313-320 References
Open Access
Issue
Wuhan Univ. J. Nat. Sci.
Volume 27, Number 4, August 2022
Page(s) 313 - 320
DOI https://doi.org/10.1051/wujns/2022274313
Published online 26 September 2022
  1. Animasaun I L, Shah N A, Wakif A, et al. Ratio of Momentum Diffusivity to Thermal Diffusivity: Introduction, Meta-analysis, and Scrutinization[M]. New York: Chapman and Hall/CRC, 2022. [Google Scholar]
  2. Cao W H, Animasaun I L, Yook S J, et al. Simulation of the dynamics of colloidal mixture of water with various nanoparticles at different levels of partial slip: Ternary-hybrid nanofluid[J]. Inter J Commun Heat Mass, 2022, 135: 106069. [CrossRef] [Google Scholar]
  3. Xia W F, Animasaun I L, Wakif A, et al. Gear-generalized differential quadrature analysis of oscillatory convective Taylor-Couette flows of second-grade fluids subject to Lorentz and Darcy-Forchheimer quadratic drag forces[J]. Inter J Commun Heat Mass, 2021, 126: 105395. [CrossRef] [Google Scholar]
  4. Chowdhury M S H, Hashim I. Application of homotopy-perturbation method to Klein-Gordon and sine-Gordon equations[J]. Chaos Soliton Fract, 2009, 39: 1928-1935. [CrossRef] [Google Scholar]
  5. Wazwaz M A. New travelling wave solutions to the Boussinesq and the Klein-Gordon equations[J]. Commun Nonlinear Sci Numer Simul, 2008, 13: 889-901. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  6. Zheng H, Zhang C Z, Wang Y S, et al. A local RBF collocation method for band structure computations of 2D solid/fluid and fluid/solid phononic crystals[J]. Int J Numer Meth Eng, 2017, 110 (5): 467-500. [NASA ADS] [CrossRef] [Google Scholar]
  7. Wang L H, Qian Z H. A meshfree stabilized collocation method (SCM) based on reproducing kernel approximation[J]. Comput Method Appl M, 2020, 371:113303. [NASA ADS] [CrossRef] [Google Scholar]
  8. Gu Y, Fan C M, Xu R P. Localized method of fundamental solutions for large-scale modelling of two-dimensional elasticity problems[J]. Appl Math Lett, 2019, 93: 8-14. [CrossRef] [MathSciNet] [Google Scholar]
  9. Lin J, Chen F, Zhang L J. An accurate meshless collocation technique for solving two-dimensional hyperbolic telegraph equations in arbitrary domains[J]. Eng Anal Bound Elem, 2019, 108: 372-384. [CrossRef] [MathSciNet] [Google Scholar]
  10. Lee I J. Numerical solution for nonlinear Klein-Gordon equation by collocation method with respect to spectral method[J]. J Korean Math Soc, 1995, 32: 541-551. [MathSciNet] [Google Scholar]
  11. Duncan D B. Symplectic finite difference approximations of the nonlinear Klein-Gordon equation[J]. SIAM J Numer Anal, 1997, 34: 1742-1760. [CrossRef] [MathSciNet] [Google Scholar]
  12. El-Sayed S M. The decomposition method for studying the Klein-Gordon equation[J]. Chaos Soliton Fract, 2003, 18: 1025-1030. [CrossRef] [Google Scholar]
  13. Hariharan G. Haar wavelet method for solving the Klein-Gordon and the Sine-Gordon equations[J]. Int J Nonlinear Sci, 2011, 11: 180-189. [Google Scholar]
  14. Pekmen B, Tezer-Sezgin M. Differential quadrature solution of nonlinear Klein-Gordon and Sine-Gordon equations[J]. Comput Phys Commun, 2012, 183: 1702-1713. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  15. Lynch MAM. Large amplitude instability in finite difference approximations to the Klein-Gordon equation[J]. Appl Numer Math, 1999, 31: 173-182. [Google Scholar]
  16. Guo B Y, Li X, Vazquez L. A Legendre spectral method for solving the nonlinear Klein-Gordon equation[J]. Math Appl Comput, 1996, 15 (1): 19-36. [Google Scholar]
  17. Li X, Guo B Y. A Legendre spectral method for solving nonlinear Klein-Gordon equation[J]. J Comput Math, 1997, 15 (2): 105-126. [MathSciNet] [Google Scholar]
  18. Zheng H, Wang F, Chen C S, et al. Improved 3D surface reconstruction via the method of fundamental solutions[J]. Numer Mathe Theory Me, 2020, 13(4): 973-985. [CrossRef] [Google Scholar]
  19. Zheng H, Xiong J G, Yuan Y, et al. Mixed-mode dynamic stress intensity factors by variation technique with finite block method[J]. Eng Anal Bound Elem, 2019, 106: 27-33. [CrossRef] [MathSciNet] [Google Scholar]
  20. Zheng H, Sladek J, Sladek V, et al. Fracture analysis of functionally graded material by hybrid meshless displacement discontinuity method[J]. Eng Fract Mech, 2021, 247: 107591. [CrossRef] [Google Scholar]
  21. Dehghan M, Shokri A. Numerical solution of the nonlinear Klein-Gordon equation using radial basis functions[J]. J Comput Appl Math, 2009, 230: 400-410. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  22. Lakestani M, Dehghan M. Collocation and finite difference-collocation methods for the solution of nonlinear Klein-Gordon equation[J]. Comput Phys Commun, 2010, 181: 1392-1401. [NASA ADS] [CrossRef] [Google Scholar]
  23. Dehghan M, Mohammadi V. Two numerical meshless techniques based on radial basis functions (RBFs) and the method of generalized moving least squares (GMLS) for simulation of coupled Klein-Gordon-Schrodinger (KGS) equations[J]. Comput Math Appl, 2016, 71: 892-921. [CrossRef] [MathSciNet] [Google Scholar]
  24. Shivanian E, Jafarabadi A. An improved meshless method for solving two- and three-dimensional coupled Klein-Gordon-Schrodinger equations on scattered data of general-shaped domains[J]. Eng Comput –GERMANY, 2018, 34: 757-774. [CrossRef] [Google Scholar]
  25. Ahmad I, Ahsan M, Hussain I, et al. Numerical simulation of PDEs by local meshless differential quadrature collocation method[J]. Symmetry-BASEL, 2019, 11(3): 394. [NASA ADS] [CrossRef] [Google Scholar]
  26. Myers D E, Iaco S D, Posa D, et al. Space-time radial basis functions[J]. Comput Math Appl, 2002, 43: 539-549. [CrossRef] [MathSciNet] [Google Scholar]
  27. Liu C, Ku C, Xiao J, et al. A novel spacetime collocation meshless method for solving two dimensional backward heat conduction problems[J]. CMES Comp Model Eng, 2019, 118(1): 229-252. [Google Scholar]
  28. Wang F Z, Chen W, Jiang X R. Investigation of regularization techniques for boundary knot method[J]. Commun Numer Meth Eng, 2010, 26: 1868-1877. [Google Scholar]
  29. Wang F Z, Chen W, Ling L. Combinations of the method of fundamental solutions for general inverse source identification problems[J]. Appl Math Comput, 2012, 219: 1173-1182. [CrossRef] [MathSciNet] [Google Scholar]
  30. Fasshauer G E, Zhang J G. On choosing optimal shape parameters for RBF approximation[J]. Numer Algorithms, 2007, 45: 345-368. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  31. Chen W, Hong Y X, Lin J. The sample solution approach for determination of the optimal shape parameter in the multiquadric function of the Kansa method[J]. Comput Math Appl, 2018, 75: 2942-2954. [CrossRef] [MathSciNet] [Google Scholar]
  32. El-Sayed S M. The decomposition method for studying the Klein-Gordon equation[J]. Chaos Soliton Fract, 2003, 18: 1025-1030. [CrossRef] [Google Scholar]
  33. Hussain A, Haq S, Uddin M. Numerical solution of Klein-Gordon and sine-Gordon equations by meshless method of lines[J]. Eng Anal Bound Elem, 2013, 37: 1351-1366. [CrossRef] [MathSciNet] [Google Scholar]
  34. Wang F Z, Hou E R, Salama S A, et al. Numerical Investigation of the nonlinear fractional Ostrovsky equation[J]. Fractals, 2022, 30(5): 22401429. [Google Scholar]
  35. Wang F Z, Khan M N, Ahmad I, et al. Numerical solution of traveling waves in chemical kinetics: Time fractional fishers equations[J]. Fractals, 2022, 30(2): 2240051. [CrossRef] [Google Scholar]

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