A New Series Solution Applicable to a Class of Boundary Layer Equations with Exponential Decay in Solution
Exponential decay; FalknerSkan-type equation; Series solution; Shooting method; Stretching sheet
A new series solution for the coupled nonlinear boundary value problem (BVP) of the FalknerSkan-type, resulting from the use of the boundary layer approximation to a mixed convective flow is obtained. The solution domain is transformed from the semi-infinite interval of physical interest to the unit interval by using the transformation z= 1 - e-?. 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 powers of 1 - e-? with assistance from the NewtonRaphson method. Convergence of the series is assured by the very design of the series as confirmed by the DombSykes 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 the RungeKuttaFehlberg45 and NewtonRaphson 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. 2020, Springer Nature India Private Limited.
International Journal of Applied and Computational Mathematics, Vol-6, No. 4
Siddheshwar P.G., Department of Mathematics, CHRIST (Deemed to be University), Hosur Road, Bengaluru, 560029, India; Narayana M., Department of Mathematics, The University of the West Indies, Mona Campus, Kingston 7, Jamaica; Bhatt B., Department of Mathematics and Statistics, The University of the West Indies, St. Augustine, Trinidad and Tobago