A seminar has been delivered by Dr. Mahesha Narayana, Senior Lecturer, Department of Mathematics, UWI Mona Campus on 25-10-2019 at Mathematics Lecture Theatre 3 (M3). In this regard please find the details as below.
Title: A new series solution applicable to a class of boundary layer equations with exponential decay in solution
Abstract: A new series solution for coupled nonlinear boundary value problem (BVP) of the Falkner-Skan-type, resulting from the use of boundary layer approximation to a mixed convective flow is obtained. The solution domain is transformed from the semi-infinite interval of the physical interest to the unit interval using a special transformation of z. The coupled nonlinear BVP is converted into an equivalent initial value problem (IVP) by supplying appropriate initial conditions. Series solution of the equivalent IVP is obtained in the powers of that transformation of z in assistance with the Newton-Raphson method. Convergence of the series is assured by the very design of the series as confirmed by the Domb-Sykes plots and the plots of partial sums. The results of the series solution compare well with the numerical results obtained by the shooting method based on Runge-Kutta-Fehlberg45 and Newton-Raphson methods. The novelty of the methodology lies in the construction of a new series solution for a class of problems with exponential decay in their solution. Such a work has not been reported before.
Keywords: Series solution, Falkner-Skan-type equation, Exponential decay, Stretching sheet, Shooting method.