International Scientific Journal


We apply reproducing kernel method to the density-dependent diffusion Nagumo equation. Powerful method has been applied by reproducing kernel functions. The approximations to the exact solution are obtained. In particular, series solutions are obtained. These solutions demonstrate the certainty of the method. The results acquired in this work conceive many attracted behaviors that assure further work on the Nagumo equation.
PAPER REVISED: 2017-11-20
PAPER ACCEPTED: 2017-11-27
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S143 - S152]
  1. Ali Akgül, Mustafa Inc, and Esra Karatas. Reproducing kernel functions for difference equations. Discrete Contin. Dyn. Syst. Ser. S, 8(6):1055-1064, 2015.
  2. Ali Akgül, Mustafa Inc, Adem Kilicman, and Dumitru Baleanu. A new approach for onedimensional sine-Gordon equation. Adv. Difference Equ., pages 2016:8, 20, 2016.
  3. Ali Akgül. New reproducing kernel functions. Math. Probl. Eng., pages Art. ID 158134, 10, 2015.
  4. N. Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68:337-404, 1950.
  5. Esmail Babolian, Shahnam Javadi, and Eslam Moradi. RKM for solving Bratu-type differential equations of fractional order. Math. Methods Appl. Sci., 39(6):1548-1557, 2016.
  6. Bariza Boutarfa, Ali Akgül, and Mustafa Inc. New approach for the Fornberg-Whitham type equations. J. Comput. Appl. Math., 312:13-26, 2017.
  7. Minggen Cui and Yingzhen Lin. Nonlinear numerical analysis in the reproducing kernel space. Nova Science Publishers Inc., New York, 2009.
  8. F. Z. Geng and Z. Q. Tang. Piecewise shooting reproducing kernel method for linear singularly perturbed boundary value problems. Appl. Math. Lett., 62:1-8, 2016.
  9. Mustafa Inc, Ali Akgül, and Fazhan Geng. Reproducing kernel Hilbert space method for solving Bratu's problem. Bull. Malays. Math. Sci. Soc., 38(1):271-287, 2015.
  10. Mehmet Giyas Sakar. Iterative reproducing kernel Hilbert spaces method for Riccati differential equations. J. Comput. Appl. Math., 309:163-174, 2017.
  11. Robert A. Van Gorder and K. Vajravelu. Analytical and numerical solutions of the density dependent diffusion Nagumo equation. Phys. Lett. A, 372(31):5152-5158, 2008.
  12. Deng-Shan Wang, Fei Chen, and Xiao-Yong Wen. Darboux transformation of the general Hirota equation: multisoliton solutions, breather solutions, and rogue wave solutions. Adv. Difference Equ., pages 2016:67, 17, 2016.
  13. Stanislav Zaremba. Sur le calcul numérique des fonctions demandées dan le probléme de dirichlet et le probleme hydrodynamique. Bulletin International l'Académia des Sciences de Cracovie, 68:125-195, 1908

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence