A RELIABLE ALGORITHM FOR SOLVING BLASIUS BOUNDARY VALUE PROBLEM
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Keywords:
Nonlinear differential equations, Blassius equation, Approximate solutions, Adomian decomposition method, laminar flowAbstract
The Blasius equation is a well-known third-order nonlinear
ordinary differential equation that can be found in some fluid dynamics boundary layer problems.
In this paper, we convert the nonlinear differential equation to an integral equation, this integral equation has
a shifted kernel. Our goal is to propose an efficient modification of the
standard Adomian decomposition method, combined with the Laplace
transform, for solving the Blasius equation. The main impediment to
solving the Blasius equation is the absence of the second derivative at
zero. Once this derivative has been correctly evaluated, an analytical
solution to the Blasius problem can be easily found; as a result, we use
our approximate solution to estimate the value of y′′(0), also known asthe
Blasius constant. Understanding the Blasius constant is essential
for calculating shear stress at a plate. Furthermore, once this value
is determined, we have the initial value problem, which can be solved
numerically
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