Transformation of boundary value problems into initial value problems

• Published in: Journal of mathematical analysis and applications Vol. 32; no. 2; pp. 308 - 330
• Main Author: Klamkin, Murray S
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.1970
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/0022-247X(70)90299-4

In a previous paper of the author (SIAM Review, 1962, pp. 43–47), the idea of Blasius for the transformation of the B.V.P., y‴ + yy′' = 0, y( o) = y′( o) = 0, y′(∞) = 2, into a pair of similar I.V.P.'s was extended to D.E.'s or systems of D.E.'s of any order which were invariant under certain groups of homogeneous linear transformations. The boundary conditions were specified at the origin and at infinity and were homogeneous at the initial point. Subsequently, T. Y. Na (SIAM Review, 1967, pp. 204–210; 1968, pp. 85–87) showed that the method was also applicable to finite intervals and also considered other groups of transformations. He noted that for the method to apply, the boundary conditions have to be homogeneous at the initial point. Here, however, we show that homogeneity is not necessary by treating equations subject to a variety of nonhomogeneous boundary conditions.