An Approximate Technique for Solving Lagerstrom Equation

Year 2020, , 101 - 108, 30.06.2020

Md. Zahangir Alam , Md. Shamsul Alam Md. Nazmul Sharif

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.

Keywords

Lagerstrom’s equation, ExpIntegralEi, Homotopy perturbation 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.