Search Advanced

AIMS Mathematics

2023, Volume 8, Issue 4: 8756-8771. doi: 10.3934/math.2023439
Previous Article Next Article
Research article Special Issues

Barycentric rational collocation method for semi-infinite domain problems

  • School of Science, Shandong Jianzhu University, Jinan, 250101, China
  • Received: 25 December 2022 Revised: 01 February 2023 Accepted: 02 February 2023 Published: 07 February 2023

  • MSC : 65D32, 65D30, 65R20

  • The barycentric rational collocation method for solving semi-infinite domain problems is presented. Following the barycentric interpolation method of rational polynomial and Chebyshev polynomial, matrix equation is obtained from discrete semi-infinite domain problem. Truncation method and transformation method are presented to solve linear and nonlinear differential equation defined on the semi-infinite domain problems. At last, three numerical examples are presented to valid our theoretical analysis.

    Citation: Jin Li. Barycentric rational collocation method for semi-infinite domain problems[J]. AIMS Mathematics, 2023, 8(4): 8756-8771. doi: 10.3934/math.2023439

    Related Papers:

  • The barycentric rational collocation method for solving semi-infinite domain problems is presented. Following the barycentric interpolation method of rational polynomial and Chebyshev polynomial, matrix equation is obtained from discrete semi-infinite domain problem. Truncation method and transformation method are presented to solve linear and nonlinear differential equation defined on the semi-infinite domain problems. At last, three numerical examples are presented to valid our theoretical analysis.


    加载中


    [1] M. Maleki, I. Hashim, S. Abbasbandy, Analysis of IVPs and BVPs on semi-infinite domains via collocation methods, J. Appl. Math., 2012 (2012), 1–21. https://doi.org/10.1155/2012/696574 doi: 10.1155/2012/696574
    [2] S. A. Odejide, Y. A. S. Aregbesola, Applications of method of weighted residuals to problems with Semi-infinite domain, Rom. J. Phys., 56 (2011), 14–24.
    [3] F. Auteri, L. Quartapelle, Galerkin-Laguerre spectral solution of self-similar boundary layer problems, Commun. Comput. Phys., 12 (2012), 1329–1358. https://doi.org/10.4208/cicp.130411.230911a doi: 10.4208/cicp.130411.230911a
    [4] A. O. Adewumi, S. O. Akindeinde, A. A. Aderogba, Laplace-weighted residual method for problems with semi-infinite domain, J. Mod. Method Numer. Math., 7 (2016), 59–66.
    [5] H. F. Ismael, H. Bulut, H. M. Baskonus, W. Gao, Dynamical behaviors to the coupled schrdinger-boussinesq system with the beta derivative, AIMS Math., 6 (2021), 7909–7928. https://doi.org/10.3934/math.2021459 doi: 10.3934/math.2021459
    [6] H. Jafari, N. Kadkhoda, D. Baleanu, Lie group theory for nonlinear fractional K(m, n) type equation with variable coefficients, Meth. Math. Model. Comput. Complex Syst., 2021,207–227. https://doi.org/10.1007/978-3-030-77169-0_8
    [7] D. Baleanu, Z. B. Guvenc, J. Machado, New trends in nanotechnology and fractional calculus applications, Springer Netherlands, 2010. https://doi.org/10.1007/978-90-481-3293-5
    [8] A. Atangana, D. Baleanu, A. Alsaedi, New properties of conformable derivative, Open Math., 13 (2015), 1–10. https://doi.org/10.1515/math-2015-0081 doi: 10.1515/math-2015-0081
    [9] Gulnur Yel, C. Cattani, H. M. Baskonus, W. Gao, On the complex simulations with dark-bright to the hirota-maccari system, J. Comput. Nonlinear Dyn., 6 (2021), 16. https://doi.org/ 10.1115/1.4050677 doi: 10.1115/1.4050677
    [10] Y. M. Li, H. M. Baskonus, A. M. Khudhur, Investigations of the complex wave patterns to the generalized calogero-bogoyavlenskii-schiff equation, Soft Comput., 25 (2021), 6999–7008. https://doi.org/10.1007/s00500-021-05627-2 doi: 10.1007/s00500-021-05627-2
    [11] S. Rashid, S. Parveen, H. Ahmad, Y. M. Chu, New quantum integral inequalities for some new classes of generalized $\phi$-convex functions and their scope in physical systems, Open Phys., 19 (2021), 35–50. https://doi.org/10.1515/phys-2021-0001 doi: 10.1515/phys-2021-0001
    [12] S. Rashid, D. Baleanu, Y. M. Chu, Some new extensions for fractional integral operator having exponential in the kernel and their applications in physical systems, Open Phys., 18 (2020), 478–491. https://doi.org/10.1515/phys-2020-0114 doi: 10.1515/phys-2020-0114
    [13] L. Xu, Y. M. Chu, S. Rashid, A. A. El-Deeb, K. S. Nisar, On new unified bounds for a family of functions via fractional-calculus theory, J. Funct. Space., 2020 (2020), 1–9. https://doi.org/10.1155/2020/4984612 doi: 10.1155/2020/4984612
    [14] S. Rashid, M. Can, D. Baleanu, M. C. Yu, Generation of new fractional inequalities via n polynomials s-type convexity with applications, Adv. Differential Equ., 2020 (2020), 1–20. https://doi.org/10.1186/S13662-020-02720-Y doi: 10.1186/S13662-020-02720-Y
    [15] S. Rashid, Z. Hammouch, D. Baleanu, M. C. Yu, New generalizations in the sense of the weighted non-singular fractional integral operator, Fractalsy, 28 (2020), 2040003. https://doi.org/10.1142/S0218348X20400034 doi: 10.1142/S0218348X20400034
    [16] S. Rashid, H. Kalsoom, Z. Hammouch, R. Ashraf, Y. M. Chu, New multi-parametrized estimates having pth-order differentiability in fractional calculus for predominating-convex functions in hilbert space, Symmetry, 12 (2020), 222. https://doi.org/10.1016/s0362-546x(01)00646-0 doi: 10.1016/s0362-546x(01)00646-0
    [17] Y. B. Yang, S. R. Kuo, H. H. Hung, Frequency-independent infinite elements for analysing semi-infinite problems, Int. J. Numer. Method Eng., 39 (1996), 3553–3569. https://doi.org/10.1002/(SICI)1097-0207(19961030)39:20<3553::AID-NME16>3.0.CO;2-6 doi: 10.1002/(SICI)1097-0207(19961030)39:20<3553::AID-NME16>3.0.CO;2-6
    [18] A. Akgül, A novel method for the solution of Blasius equation in semi-infinite domains, IJOCTA, 7 (2017), 225–233. https://doi.org/10.11121/ijocta.01.2017.00363 doi: 10.11121/ijocta.01.2017.00363
    [19] P. Berrut, M. S. Floater, G. Klein, Convergence rates of derivatives of a family of barycentric rational interpolants, Appl. Numer. Math., 61 (2011), 989–1000. https://doi.org/10.1016/j.apnum.2011.05.001 doi: 10.1016/j.apnum.2011.05.001
    [20] J. P. Berrut, S. A. Hosseini, G. Klein, The linear barycentric rational quadrature method for Volterra integral equations, SIAM J. Sci. Comput., 36 (2014), 105–123. https://doi.org/10.1137/120904020 doi: 10.1137/120904020
    [21] M. Floater, H. Kai, Barycentric rational interpolation with no poles and high rates of approximation, Numer. Math., 107 (2007), 315–331. https://doi.org/10.1007/s00211-007-0093-y doi: 10.1007/s00211-007-0093-y
    [22] G. Klein, J. Berrut, Linear rational finite differences from derivatives of barycentric rational interpolants, SIAM J. Numer. Anal., 50 (2012), 643–656. https://doi.org/10.1137/110827156 doi: 10.1137/110827156
    [23] G. Klein, J. Berrut, Linear barycentric rational quadrature, BIT Numer. Math., 52 (2012), 407–424. https://doi.org/10.1007/s10543-011-0357-x doi: 10.1007/s10543-011-0357-x
    [24] L. H. Wang, M. H. Hu, Z. Zhong, F. Yang, Stabilized lagrange interpolation collocation method: A meshfree method incorporating the advantages of finite element method, Comput. Method. Appl. M., 404 (2023), 115780. https://doi.org/10.1016/j.cma.2022.115780 doi: 10.1016/j.cma.2022.115780
    [25] Z. H. Qian, L. H. Wang, A meshfree stabilized collocation method (SCM) based on reproducing kernel approximation, Comput. Method. Appl. M., 371 (2020), 113303. https://doi.org/10.1016/j.cma.2020.113303 doi: 10.1016/j.cma.2020.113303
    [26] Z. H. Qian, L. H. Wang, Y. Gu, C. Z. Zhang, An efficient meshfree gradient smoothing collocation method (GSCM) using reproducing kernel approximation, Comput. Method. Appl. M., 374 (2021), 113573. https://doi.org/10.1016/j.cma.2020.113573 doi: 10.1016/j.cma.2020.113573
    [27] M. N. Rasoulizadeh, M. J. Ebadi, Z. Avazzadeh, O. Nikan, An efficient local meshless method for the equal width equation in fluid mechanics, Eng. Anal. Bound. Elem., 131 (2021), 258–268. https://doi.org/10.1016/j.enganabound.2021.07.001 doi: 10.1016/j.enganabound.2021.07.001
    [28] O. Nikan, Avazzadeh, An efficient localized meshless technique for approximating nonlinear sinh-Gordon equation arising in surface theory, Eng. Anal. Bound. Elem., 130 (2021), 268–285. https://doi.org/10.1016/j.enganabound.2021.05.019 doi: 10.1016/j.enganabound.2021.05.019
    [29] O. Nikan, Z. Avazzadeh, A locally stabilized radial basis function partition of unity technique for the sine-Gordon system in nonlinear optics, Math. Comput. Simul., 199 (2022), 394–413. https://doi.org/10.1016/j.matcom.2022.04.006 doi: 10.1016/j.matcom.2022.04.006
    [30] O. Nikan, Z. Avazzadeh, M. N. Rasoulizadeh, Soliton wave solutions of nonlinear mathematical models in elastic rods and bistable surfaces, Eng. Anal. Bound. Elem., 143 (2022), 14–27. https://doi.org/10.1016/j.enganabound.2022.05.026 doi: 10.1016/j.enganabound.2022.05.026
    [31] O. Nikan, Z. Avazzadeh, M. N. Rasoulizadeh, Soliton solutions of the nonlinear sine-Gordon model with Neumann boundary conditions arising in crystal dislocation theory, Nonlinear Dyn., 106 (2021), 783–813. https://doi.org/10.1007/s11071-021-06822-4 doi: 10.1007/s11071-021-06822-4
    [32] Z. Avazzadeh, O. Nikan, J. A. T. Machado, Solitary wave solutions of the generalized Rosenau-KdV-RLW equation, Mathematics, 8 (2020), 1601. https://doi.org/10.3390/math8091601 doi: 10.3390/math8091601
    [33] J. Li, Y. Cheng, Linear barycentric rational collocation method for solving heat conduction equation, Numer. Meth. Part. D. E., 37 (2021), 533–545. https://doi.org/10.1002/num.22539 doi: 10.1002/num.22539
    [34] J. Li, Y. Cheng, Linear barycentric rational collocation method for solving second-order Volterra integro-differential equation, Comput. Appl. Math., 39 (2020). https://doi.org/10.1007/s40314-020-1114-z
    [35] J. Li, Y. L. Cheng, Z. C. Li, Z. K. Tian, Linear barycentric rational collocation method for solving generalized Poisson equations, MBE, 20 (2023), 4782–4797. https://doi.org/10.3934/mbe.2023221 doi: 10.3934/mbe.2023221
    [36] J. Li, Y. Cheng, Barycentric rational method for solving biharmonic equation by depression of order, Numer. Meth. Part. D. E., 37 (2021), 1993–2007. https://doi.org/10.1002/num.22638 doi: 10.1002/num.22638
    [37] Z. Wang, S. Li, Barycentric interpolation collocation method for nonlinear problems, National Defense Industry Press, Beijing, 2015.
    [38] Z. Wang, Z. Xu, J. Li, Mixed barycentric interpolation collocation method of displacement-pressure for incompressible plane elastic problems, Chin. J. Appl. Mech., 35 (2018), 195–201.
    [39] Z. Wang, L. Zhang, Z. Xu, J. Li, Barycentric interpolation collocation method based on mixed displacement-stress formulation for solving plane elastic problems, Chin. J. Appl. Mech., 35 (2018), 304–309.
  • Reader Comments
  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(1298) PDF downloads(71) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline

Figures and Tables

Tables(15)

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog