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

Year 2017, Volume: 2 Issue: 3, 37 - 44, 30.10.2017
https://doi.org/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.

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 distributedparameter systems, IEE Proc.: Part D 144 (1) 87–94.
  • Chowdhury, M. S. H., Hashim, I., (2009) Solutions of Emden–Fowler equations by homotopyperturbation 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.
Year 2017, Volume: 2 Issue: 3, 37 - 44, 30.10.2017
https://doi.org/10.28978/nesciences.349267

Abstract

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 distributedparameter systems, IEE Proc.: Part D 144 (1) 87–94.
  • Chowdhury, M. S. H., Hashim, I., (2009) Solutions of Emden–Fowler equations by homotopyperturbation 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.
There are 16 citations in total.

Details

Subjects Engineering
Journal Section 2
Authors

Sertan Alkan

Publication Date October 30, 2017
Submission Date November 4, 2017
Published in Issue Year 2017 Volume: 2 Issue: 3

Cite

APA Alkan, S. (2017). Haar wavelet collocation method for the approximate solutions of Emden-Fowler type equations. Natural and Engineering Sciences, 2(3), 37-44. https://doi.org/10.28978/nesciences.349267

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