Details

Autor(en) / Beteiligte

• Costin, O.
• Tanveer, S.

Titel

Analytical Approximation of the Blasius Similarity Solution with Rigorous Error Bounds

Ist Teil von

• SIAM journal on mathematical analysis, 2014-01, Vol.46 (6), p.3782-3813

Erscheinungsjahr

2014

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We use a recently developed method [O. Costin, M. Huang, and W. Schlag, Nonlinearity , 25 (2012), pp. 125--164], [O. Costin, M. Huang, and S. Tanveer, Duke Math. J. , 163 (2014), pp. 665--704] to find accurate analytic approximations with rigorous error bounds for the classic similarity solution of Blasius of the boundary layer equation in fluid mechanics, the two-point boundary value problem $f\prime \prime \prime} + f f\prime \prime} =0$ with $f(0)=f logical or prime (0)=0$ and $\lim_{x \rightarrow \infty} f logical or prime (x) =1$. The approximation is given in terms of a polynomial in $[0, \frac{5}{2}]$ and in terms of the error function in $[\frac{5}{2}, \infty)$. The two representations for the solution in different domains match at $x=\frac{5}{2}$ determining all free parameters in the problem, in particular $f\prime \prime} (0) =0.469600 \pm 0.000022$ at the wall. The method can in principle provide approximations to any desired accuracy for this or wide classes of linear or nonlinear differential equations with initial or boundary value conditions. The analysis relies on controlling the errors in the approximation through contraction mapping arguments, using energy bounds for the Green's function of the linearized problem.