User:Riccardofazio

Boundary value problems for Ordinary Differential Equations. For a boundary value problem (BVP) we need to specify a governing differential equation, at least of second order, and a suitable number of boundary conditions. Several books are available for the theory of BVPs, see for instace [1-4]. As an example let us show the celebrated Blasius problem [5] of boundary layer theory [6]. This boundary problem is governed by a third order differential equation to be solved along with two omogeneous boundary conditions at the origin and a non-omogeneous asymptotic boundary condition (please, forgot me if I use the LaTeX encoding, this would be friendly if you would like to insert the Blasius problem in a manuscript). \frac{d^3f}{d\eta^3} + f \frac{d^2f}{d\eta^2} = 0 f(0) = \frec{df}{d\eta}(0) = 0 \,        \frac{df}{d\eta}(\eta \rightarrow \infty) = 1 \.

[1] A.S. Fokas, A Unified Approach to Boundary Value Problems, SIAM, 2008 [2] F.D. Gakhov, Boundary Value Problems, Pergamon Press, 1966. [3] H.B. Keller, Numerical Solution of two Point Boundary Value Problems, SIAM,1976. [4] D.L. Powers, Boundary Value Problems, 4th edition, Elsevier, 2014. [5] H. Blasius, Grenzschichten in Fluessigkeiten mit kleiner Reibung, Z. Math. Phys., 56, 1-37, 1908. [6] L. Prandtl, Ueber Fluessigkeiten mit kleiner Reibung, Procs. Third Inter. Math. Congr., 484-494, 1904.