Perturbed Differential Equations with Singular Points

Abstract

Here, we generalize the boundary layer functions method (or composite asymptotic expansion) for bisingular perturbed differential equations (BPDE that is perturbed differential equations with singular point). We will construct a uniform valid asymptotic solution of the singularly perturbed first-order equation with a turning point, for BPDE of the Airy type and for BPDE of the second-order with a regularly singular point, and for the boundary value problem of Cole equation with a weak singularity.A uniform valid expansion of solution of Lighthill model equation by the method of uniformization and the explicit solution-this one by the generalization method of the boundary layer function-is constructed. Furthermore, we construct a uniformly convergent solution of the Lagerstrom model equation by the method of fictitious parameter.

An Approximate Technique for Solving Lagerstrom Equation

“…S. Kaplun and P. A. Lagerstrom [6] have presented asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers. N. Fenichel [7], K. K. Alymkulov and D. A. Tursunov [8], P. A. Lagerstrom and R. G. Casten [9] used singular perturbation technique for solving ordinary differential equation. Lagerstrom's model equation is given by the non-autonomous second-order boundary value problem…”

Сингулярдуу Козголгон Өзгөчө Чекити Бар Биринчи Тартиптеги Дифференциалдык Теңдеменин Чечиминин Асимптотикасын Тургузуу

“…Өзгөчө Лайтхилл түрүндөгү биринчи жана экинчи тартиптеги теңдемелери үчүн жалпыланган чекара усулу[1], кеңейтүү усулу[2] жана униформизациялоо усулдарын колдонсо болот.…”