Abstract
In this paper, we study the nonlinear boundary-layer equation of Falkner- Skan defned on a semi-infnite domain. An iterative finite difference (IFD) scheme is proposed to numerically solve such nonlinear ordinary differential equation. A computational iterative scheme is developed based on Newton-Kantorovich quasilinearization. At every iteration, the obtained linearized differential equation is numerically solved using the standard finite difference method. Numerical experiments show the accuracy and efficiency of the method compared to existing solvers. The computation is performed for different parameter values, including the special case of Blasius problem.
Highlights
The numerical solution for nonlinear differential equations is a major problem in computational mathematics
One known nonlinear differential equation defined on a semi-infinite domain is the so-called Blasius equation which appeared in the literature in 1908 [4]
In order to solve the resulting nonlinear integro-differential equation, we develop an iterative scheme based on Newton-Raphson-Kantorovich method in function space [3, 28] combined with the standard finite difference method
Summary
The numerical solution for nonlinear differential equations is a major problem in computational mathematics. Mukhopadhyay et al [18] investigated a boundary-layer forced convection flow of a Casson fluid past a symmetric wedge Despite these aforementioned research work since the beginning of the previous century, there is no closed-form solutions available for Falkner-Skan problem nor for the special case of Blasius problem. This fact stimulated researchers to investigate for most reliable, efficient, and low-computation cost solutions. In this manuscript, we introduce a new coordinate transformation and we apply it to Falkner-Skan problem (1.1) in order to overcome the difficulty of the semi-infinite domain. Numerical simulations will be performed to demonstrate the efficiency and reliability of the proposed numerical solver in producing accurate solutions with low computation cost
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
