Journal of Optimization Theory and Applications

, Volume 40, Issue 3, pp 397–403

Boundary conditions of the second-order differential equation and the Riccati equation


  • S. M. Roberts
    • IBM Palo Alto Scientific Center
Contributed Papers

DOI: 10.1007/BF00933507

Cite this article as:
Roberts, S.M. J Optim Theory Appl (1983) 40: 397. doi:10.1007/BF00933507


The conversion of a second-order linear ordinary differential equation with variable coefficients into a Riccati equation depends on whether the second-order problem is an initial-value or two-point boundary-value problem. The distinction is critical in determining the initial condition for the Riccati equation. If the second-order problem is an initial-value problem, the choice of the Riccati transformation depends on whether a zero initial condition for the function or its derivative is specified. If the problem is a two-point boundary-value problem, special methods must be introduced as described in the paper.

Key Words

Riccati equationsecond-order ordinary differential equationinitial-value problemtwo-point boundary-value problemmethod of adjointsinvariant imbeddingScott's method

Copyright information

© Plenum Publishing Corporation 1983