scholarly journals On Solving the Nonlinear Falkner–Skan Boundary-Value Problem: A Review

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 153
Author(s):  
Asai Asaithambi
Keyword(s):  
Boundary Layer ◽  
Mixed Methods ◽  
Boundary Value Problem ◽  
Velocity Distribution ◽  
Laminar Boundary Layer ◽  
Boundary Value ◽  
Third Order ◽  
Ongoing Research ◽  
The Third

This article is a review of ongoing research on analytical, numerical, and mixed methods for the solution of the third-order nonlinear Falkner–Skan boundary-value problem, which models the non-dimensional velocity distribution in the laminar boundary layer.

ON THE SOLUTIONS OF NONLINEAR THIRD ORDER BOUNDARY VALUE PROBLEMS

2010 ◽  
Vol 15 (1) ◽  
pp. 127-136
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Order Equation ◽  
Structure Of Solutions ◽  
Third Order ◽  
Number Of Solutions ◽  
The Third

The author considers a three‐point third order boundary value problem. Properties and the structure of solutions of the third order equation are discussed. Also, a connection between the number of solutions of the boundary value problem and the structure of solutions of the equation is established.

scholarly journals Approximations With Polynomial, Trigonometric, Exponential Splines of the Third Order and Boundary Value Problem

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Problem ◽  
Order Approximation ◽  
Boundary Value ◽  
Numerical Differentiation ◽  
Polynomial Splines ◽  
Third Order ◽  
Numerical Examples ◽  
The Third ◽  
Trigonometric Splines

This paper is devoted to the construction of localapproximations of functions of one and two variables using thepolynomial, the trigonometric, and the exponential splines. Thesesplines are useful for visualizing flows of graphic information.Here, we also discuss the parallelization of computations. Someattention is paid to obtaining two-sided estimates of theapproximations using interval analysis methods. Particularattention is paid to solving the boundary value problem by usingthe polynomial splines and the trigonometric splines of the thirdand fourth order approximation. Using the considered splines,formulas for a numerical differentiation are constructed. Theseformulas are used to construct computational schemes for solvinga parabolic problem. Questions of approximation and stability ofthe obtained schemes are considered. Numerical examples arepresented.

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