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Representation for the reproducing kernel Hilbert space method for a nonlinear system

Yıl 2019, Cilt: 48 Sayı: 5, 1345 - 1355, 08.10.2019

Öz

We apply the reproducing kernel Hilbert space method to a nonlinear system in this work. We utilize this  technique to overcome the nonlinearity of the problem. We obtain accurate results. We demonstrate our results by tables and figures. We prove the efficiency of the method.

Kaynakça

  • [1] S. Abbasbandy, B. Azarnavid and M. S. Alhuthali, A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems, J. Comput. Appl. Math., 279, 293–305, 2015.
  • [2] A. Akgul and M. Inc, Approximate solutions for mhd squeezing fluid flow by a novel method, Boundary Value Problems, 2014, Article number: 18, 2014.
  • [3] B. Azarnavid and K. Parand, An iterative reproducing kernel method in Hilbert space for the multi-point boundary value problems, J. Comput. Appl. Math., 328, 151–163, 2018.
  • [4] A. H. Bhrawy, M. A. Abdelkawy, E. M. Hilal, A. A. Alshaery and A. Biswas, Solitons, cnoidal waves, snoidal waves and other solutions to Whitham-Broer-Kaup system, Appl. Math. Inf. Sci., 8 (5), 2119–2128, 2014, doi:10.12785/amis/080505.
  • [5] A. H. Bhrawy, J. F. Alzaidy, M. A. Abdelkawy and A. Biswas, Jacobi spectral collocation approximation for multi-dimensional time-fractional Schrödinger equations, Nonlinear Dynam., 84 (3), 1553–1567, 2016, doi:10.1007/s11071-015-2588-x.
  • [6] A. Biswas, Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients, Nonlinear Dynam., 58 (1-2), 345–348, 2009, doi:10.1007/ s11071-009-9480-5.
  • [7] D. Biswas and T. Banerjee, A simple chaotic and hyperchaotic time-delay system: design and electronic circuit implementation, Nonlinear Dynam., 83 (4), 2331–2347, 2016, doi:10.1007/s11071-015-2484-4.
  • [8] S. Choi and J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticle, ASME FED, 231, 99–105, 1995.
  • [9] I. Cialenco, G. E. Fasshauer and Q. Ye, Approximation of stochastic partial differential equations by a kernel-based collocation method, Int. J. Comput. Math., 89 (18), 2543– 2561, 2012.
  • [10] M. Cui and Y. Lin, Nonlinear numerical analysis in the reproducing kernel space, Nova Science Publishers Inc., New York, 2009.
  • [11] G. E. Fasshauer, F. J. Hickernell and Q. Ye, Solving support vector machines in reproducing kernel Banach spaces with positive definite functions, Appl. Comput. Harmon. Anal., 38 (1), 115–139, 2015.
  • [12] F. Geng and M. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl., 327 (2), 1167–1181, 2007, doi:10.1016/j.jmaa.2006. 05.011.
  • [13] M. Inc, A. Akgul and A. Kilicman, Numerical solutions of the second-order onedimensional telegraph equation based on reproducing kernel Hilbert space method, Abstr. Appl. Anal., 2013, 13 pages, 2013.
  • [14] R. Ketabchi, R. Mokhtari and E. Babolian, Some error estimates for solving volterra integral equations by using the reproducing kernel method, J. Comput. Appl. Math., 273, 245–250, 2015.
  • [15] K. Khanafer, K. Vafai and M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Tran., 46, 3639– 3653, 2003.
  • [16] M. Pantzali, A. Mouza and S. Paras, Investigating the efficacy of nanofluids as coolants in plate heat exchangers (phe), Chem. Eng. Sci., 64, 3290–3300, 2009.
Yıl 2019, Cilt: 48 Sayı: 5, 1345 - 1355, 08.10.2019

Öz

Kaynakça

  • [1] S. Abbasbandy, B. Azarnavid and M. S. Alhuthali, A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems, J. Comput. Appl. Math., 279, 293–305, 2015.
  • [2] A. Akgul and M. Inc, Approximate solutions for mhd squeezing fluid flow by a novel method, Boundary Value Problems, 2014, Article number: 18, 2014.
  • [3] B. Azarnavid and K. Parand, An iterative reproducing kernel method in Hilbert space for the multi-point boundary value problems, J. Comput. Appl. Math., 328, 151–163, 2018.
  • [4] A. H. Bhrawy, M. A. Abdelkawy, E. M. Hilal, A. A. Alshaery and A. Biswas, Solitons, cnoidal waves, snoidal waves and other solutions to Whitham-Broer-Kaup system, Appl. Math. Inf. Sci., 8 (5), 2119–2128, 2014, doi:10.12785/amis/080505.
  • [5] A. H. Bhrawy, J. F. Alzaidy, M. A. Abdelkawy and A. Biswas, Jacobi spectral collocation approximation for multi-dimensional time-fractional Schrödinger equations, Nonlinear Dynam., 84 (3), 1553–1567, 2016, doi:10.1007/s11071-015-2588-x.
  • [6] A. Biswas, Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients, Nonlinear Dynam., 58 (1-2), 345–348, 2009, doi:10.1007/ s11071-009-9480-5.
  • [7] D. Biswas and T. Banerjee, A simple chaotic and hyperchaotic time-delay system: design and electronic circuit implementation, Nonlinear Dynam., 83 (4), 2331–2347, 2016, doi:10.1007/s11071-015-2484-4.
  • [8] S. Choi and J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticle, ASME FED, 231, 99–105, 1995.
  • [9] I. Cialenco, G. E. Fasshauer and Q. Ye, Approximation of stochastic partial differential equations by a kernel-based collocation method, Int. J. Comput. Math., 89 (18), 2543– 2561, 2012.
  • [10] M. Cui and Y. Lin, Nonlinear numerical analysis in the reproducing kernel space, Nova Science Publishers Inc., New York, 2009.
  • [11] G. E. Fasshauer, F. J. Hickernell and Q. Ye, Solving support vector machines in reproducing kernel Banach spaces with positive definite functions, Appl. Comput. Harmon. Anal., 38 (1), 115–139, 2015.
  • [12] F. Geng and M. Cui, Solving a nonlinear system of second order boundary value problems, J. Math. Anal. Appl., 327 (2), 1167–1181, 2007, doi:10.1016/j.jmaa.2006. 05.011.
  • [13] M. Inc, A. Akgul and A. Kilicman, Numerical solutions of the second-order onedimensional telegraph equation based on reproducing kernel Hilbert space method, Abstr. Appl. Anal., 2013, 13 pages, 2013.
  • [14] R. Ketabchi, R. Mokhtari and E. Babolian, Some error estimates for solving volterra integral equations by using the reproducing kernel method, J. Comput. Appl. Math., 273, 245–250, 2015.
  • [15] K. Khanafer, K. Vafai and M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Tran., 46, 3639– 3653, 2003.
  • [16] M. Pantzali, A. Mouza and S. Paras, Investigating the efficacy of nanofluids as coolants in plate heat exchangers (phe), Chem. Eng. Sci., 64, 3290–3300, 2009.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Esra Karatas Akgül Bu kişi benim 0000-0003-3205-2393

Ali Akgül 0000-0001-9832-1424

Yasir Khan Bu kişi benim 0000-0002-6386-6181

Dumitru Baleanu 0000-0002-0286-7244

Yayımlanma Tarihi 8 Ekim 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 48 Sayı: 5

Kaynak Göster

APA Karatas Akgül, E., Akgül, A., Khan, Y., Baleanu, D. (2019). Representation for the reproducing kernel Hilbert space method for a nonlinear system. Hacettepe Journal of Mathematics and Statistics, 48(5), 1345-1355.
AMA Karatas Akgül E, Akgül A, Khan Y, Baleanu D. Representation for the reproducing kernel Hilbert space method for a nonlinear system. Hacettepe Journal of Mathematics and Statistics. Ekim 2019;48(5):1345-1355.
Chicago Karatas Akgül, Esra, Ali Akgül, Yasir Khan, ve Dumitru Baleanu. “Representation for the Reproducing Kernel Hilbert Space Method for a Nonlinear System”. Hacettepe Journal of Mathematics and Statistics 48, sy. 5 (Ekim 2019): 1345-55.
EndNote Karatas Akgül E, Akgül A, Khan Y, Baleanu D (01 Ekim 2019) Representation for the reproducing kernel Hilbert space method for a nonlinear system. Hacettepe Journal of Mathematics and Statistics 48 5 1345–1355.
IEEE E. Karatas Akgül, A. Akgül, Y. Khan, ve D. Baleanu, “Representation for the reproducing kernel Hilbert space method for a nonlinear system”, Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 5, ss. 1345–1355, 2019.
ISNAD Karatas Akgül, Esra vd. “Representation for the Reproducing Kernel Hilbert Space Method for a Nonlinear System”. Hacettepe Journal of Mathematics and Statistics 48/5 (Ekim 2019), 1345-1355.
JAMA Karatas Akgül E, Akgül A, Khan Y, Baleanu D. Representation for the reproducing kernel Hilbert space method for a nonlinear system. Hacettepe Journal of Mathematics and Statistics. 2019;48:1345–1355.
MLA Karatas Akgül, Esra vd. “Representation for the Reproducing Kernel Hilbert Space Method for a Nonlinear System”. Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 5, 2019, ss. 1345-5.
Vancouver Karatas Akgül E, Akgül A, Khan Y, Baleanu D. Representation for the reproducing kernel Hilbert space method for a nonlinear system. Hacettepe Journal of Mathematics and Statistics. 2019;48(5):1345-5.