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Haar wavelet collocation method for the approximate solutions of Emden-Fowler type equations

Sertan Alkan*

DOI: 10.28978/nesciences.349267

Abstract

This paper investigates the Haar wavelet collocation method (HWCM) to obtain approximate solution of the linear Emden-Fowler type equations. To show the efficiency and accuracy of the proposed method, some problems are solved and the obtained solutions are compared with the approximate solutions obtained by using the other numerical methods as well as the exact solutions of the problems.

Keywords

Haar wavelet collocation method, linear Emden-Fowler type equations, initial value problems

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References
  • Ahamed, M. S., Hasan, M.K. , Alam, M. S., (2017) A New Approach to Homotopy Perturbation Method for Solving Emden–Fowler Equations., Applied Mathematical Sciences 11.40: 1955-1964.
  • Bataineh, A. S., Mohd, S. M. N., Hashim, I., (2009) Homotopy analysis method for singular IVPs of Emden–Fowler type. Communications in Nonlinear Science and Numerical Simulation 14.: 1121-1131.
  • Chang, P., Piau, P, (2008) Haar wavelet matrices designation in numerical solution of ordinary differential equations, IAENG International Journal of Applied Mathematics 38.3 (2008): 164-168.
  • Chen, C.F., Hsiao, C.H., (1997) Haar wavelet method for solving lumped and distributed-parameter systems, IEE Proc.: Part D 144 (1) 87–94.
  • Chowdhury, M. S. H., Hashim, I., (2009) Solutions of Emden–Fowler equations by homotopy-perturbation method. Nonlinear Analysis: Real World Applications 10.1: 104-115.
  • Hsiao, C. H., (2004) Haar wavelet approach to linear stiff systems. Mathematics and Computers in Simulation vol 64, pp. 561-567.
  • Ibis, B., (2012) Approximate analytical solutions for nonlinear Emden-Fowler type equations by differential transform method. arXiv preprint arXiv:1211.3521.
  • Iqbal, S., Javed, A., (2011) Application of optimal homotopy asymptotic method for the analytic solution of singular Lane–Emden type equation. Applied Mathematics and Computation 217.19: 7753-7761.
  • Lepik, U., (2008) Haar wavelet method for solving higher order differential equations Int. J. Math. Comput 1 : 84-94.
  • Lepik, U., (2005) Numerical solution of differential equations using Haar wavelets. Mathematics and Computers in Simulation vol 68, pp. 127-143.
  • Lepik, U., (2009) Solving fractional integral equations by the Haar wavelet method, Appl. Math. Comput. 214: 468–478.
  • Li, Y., Zhao, W., (2010) Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations, Appl. Math. Comput. 216 2276–2285.
  • Rehman, M. U., Khan, R. A., A., (2012) numerical method for solving boundary value problems for fractional differential equations. Applied Mathematical Modelling, 36(3), 894-907.
  • Tabrizidooz, H. R., Marzban, H. R., Razzaghi, M., (2009) Solution of the generalized Emden–Fowler equations by the hybrid functions method. Physica Scripta 80.2: 025001.
  • Wazwaz, A. M., Rach, R., Bougoffa, L., Duan, J. S., (2014) Solving the Lane–Emden–Fowler type equations of higher orders by the Adomian decomposition method. Comput. Model. Eng. Sci.(CMES) 100.6: 507-529.
  • Wazwaz, A.M., (2005) Adomian decomposition method for a reliable treatment of the Emden–Fowler equation”, Appl. Math. Comput. 161, 543–560.
  • Wazwaz, A.M., (2005) Analytical solution for the time-dependent Emden–Fowler type of equations by Adomian decomposition method, Appl. Math.Comput. 166 (2005) 638–651.
  • Wazwaz, A.M., (2015) Solving Two Emden-Fowler Type Equations of Third Order by the Variational Iteration Method. Applied Mathematics & Information Sciences 9.5: 2429.