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Year 2020, Volume: 3 Issue: 2, 101 - 108, 30.06.2020
https://doi.org/10.33434/cams.712571

Abstract

References

  • [1] A. H. Nayfeh, Perturbation Method, John Wiley & Sons, New York, 1973.
  • [2] A. H. Nayfeh, D. T. Mook, Nonlinear oscillations, John Wiley & Sons, New York, 1979.
  • [3] P. A. Lagerstrom, Matched asymptotic expansions: ideas and techniques, Applied Mathematical sciences, Springer-verlag, New York, 76, 1988.
  • [4] N. Popovic, P. Szmolyan, A geometric analysis of the Lagerstrom model problem, J. Diff. Eqs., 199(2) (2004), 290-325.
  • [5] N. Popovic, P. Szmolyan, Rigorous asymptotic expansions for Lagerstrom’s model equation—a geometric approach, Nonlinear Analysis, 59 (2004), 531–565.
  • [6] S. Kaplun, P.A. Lagerstrom, Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers, J. Math. Mech., 6 (1957), 585-593.
  • [7] N. Fenichel, Geometric Singular Perturbation Theory for Ordinary Differential Equations, J. Diff. Eqs., 31 (1979), 53-98.
  • [8] K. K. Alymkulov, D. A. Tursunov, Perturbed Differential Equations with Singular Points, Perturbation Theory, Dimo I, Uzunov, Intech Open, London, UK, 2017.
  • [9] P. A. Lagerstrom, R. G. Casten, Basic concepts underlying singular perturbation techniques, SIAM rev., 14(1) (1972), 63-120.
  • [10] P. A. Lagerstrom, A course on perturbation methods, Lecture Notes by M. Mortell, National University of Ireland, Cork, 1966.
  • [11] J. He, Homotopy perturbation method: A new nonlinear analytical technique, Applied Mathematics and Computational, 135 (2003), 73-79.
  • [12] J. He, Variational iteration method-Some recent results and new interpretations, Journal of Computational and applied Mathematics, 207 ( 2007), 3-17.

An Approximate Technique for Solving Lagerstrom Equation

Year 2020, Volume: 3 Issue: 2, 101 - 108, 30.06.2020
https://doi.org/10.33434/cams.712571

Abstract

The Lagerstrom’s equation has been solved by an approximate technique combining both homotopy perturbation and variational iteration method. By this technique the solution of Lagerstrom’s equation can be determined for viscous flow past a solid at low Reynolds number where a significance mater is the occurrence of logarithmic term. In this technique ExpIntegralEi function has been used for simplifying the calculation. The results have been calculated by this technique shows a good agreement with those obtained by numerical method.

References

  • [1] A. H. Nayfeh, Perturbation Method, John Wiley & Sons, New York, 1973.
  • [2] A. H. Nayfeh, D. T. Mook, Nonlinear oscillations, John Wiley & Sons, New York, 1979.
  • [3] P. A. Lagerstrom, Matched asymptotic expansions: ideas and techniques, Applied Mathematical sciences, Springer-verlag, New York, 76, 1988.
  • [4] N. Popovic, P. Szmolyan, A geometric analysis of the Lagerstrom model problem, J. Diff. Eqs., 199(2) (2004), 290-325.
  • [5] N. Popovic, P. Szmolyan, Rigorous asymptotic expansions for Lagerstrom’s model equation—a geometric approach, Nonlinear Analysis, 59 (2004), 531–565.
  • [6] S. Kaplun, P.A. Lagerstrom, Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers, J. Math. Mech., 6 (1957), 585-593.
  • [7] N. Fenichel, Geometric Singular Perturbation Theory for Ordinary Differential Equations, J. Diff. Eqs., 31 (1979), 53-98.
  • [8] K. K. Alymkulov, D. A. Tursunov, Perturbed Differential Equations with Singular Points, Perturbation Theory, Dimo I, Uzunov, Intech Open, London, UK, 2017.
  • [9] P. A. Lagerstrom, R. G. Casten, Basic concepts underlying singular perturbation techniques, SIAM rev., 14(1) (1972), 63-120.
  • [10] P. A. Lagerstrom, A course on perturbation methods, Lecture Notes by M. Mortell, National University of Ireland, Cork, 1966.
  • [11] J. He, Homotopy perturbation method: A new nonlinear analytical technique, Applied Mathematics and Computational, 135 (2003), 73-79.
  • [12] J. He, Variational iteration method-Some recent results and new interpretations, Journal of Computational and applied Mathematics, 207 ( 2007), 3-17.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Md. Zahangir Alam 0000-0003-0128-6920

Md. Shamsul Alam This is me 0000-0002-6325-6797

Md. Nazmul Sharif 0000-0003-4234-6651

Publication Date June 30, 2020
Submission Date April 1, 2020
Acceptance Date June 24, 2020
Published in Issue Year 2020 Volume: 3 Issue: 2

Cite

APA Alam, M. Z., Alam, M. S., & Sharif, M. N. (2020). An Approximate Technique for Solving Lagerstrom Equation. Communications in Advanced Mathematical Sciences, 3(2), 101-108. https://doi.org/10.33434/cams.712571
AMA Alam MZ, Alam MS, Sharif MN. An Approximate Technique for Solving Lagerstrom Equation. Communications in Advanced Mathematical Sciences. June 2020;3(2):101-108. doi:10.33434/cams.712571
Chicago Alam, Md. Zahangir, Md. Shamsul Alam, and Md. Nazmul Sharif. “An Approximate Technique for Solving Lagerstrom Equation”. Communications in Advanced Mathematical Sciences 3, no. 2 (June 2020): 101-8. https://doi.org/10.33434/cams.712571.
EndNote Alam MZ, Alam MS, Sharif MN (June 1, 2020) An Approximate Technique for Solving Lagerstrom Equation. Communications in Advanced Mathematical Sciences 3 2 101–108.
IEEE M. Z. Alam, M. S. Alam, and M. N. Sharif, “An Approximate Technique for Solving Lagerstrom Equation”, Communications in Advanced Mathematical Sciences, vol. 3, no. 2, pp. 101–108, 2020, doi: 10.33434/cams.712571.
ISNAD Alam, Md. Zahangir et al. “An Approximate Technique for Solving Lagerstrom Equation”. Communications in Advanced Mathematical Sciences 3/2 (June 2020), 101-108. https://doi.org/10.33434/cams.712571.
JAMA Alam MZ, Alam MS, Sharif MN. An Approximate Technique for Solving Lagerstrom Equation. Communications in Advanced Mathematical Sciences. 2020;3:101–108.
MLA Alam, Md. Zahangir et al. “An Approximate Technique for Solving Lagerstrom Equation”. Communications in Advanced Mathematical Sciences, vol. 3, no. 2, 2020, pp. 101-8, doi:10.33434/cams.712571.
Vancouver Alam MZ, Alam MS, Sharif MN. An Approximate Technique for Solving Lagerstrom Equation. Communications in Advanced Mathematical Sciences. 2020;3(2):101-8.

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