Boundary conditions of the second-order differential equation and the Riccati equation
- S. M. Roberts
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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.
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- Boundary conditions of the second-order differential equation and the Riccati equation
Journal of Optimization Theory and Applications
Volume 40, Issue 3 , pp 397-403
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- Riccati equation
- second-order ordinary differential equation
- initial-value problem
- two-point boundary-value problem
- method of adjoints
- invariant imbedding
- Scott's method
- Industry Sectors
- S. M. Roberts (1)
- Author Affiliations
- 1. IBM Palo Alto Scientific Center, Palo Alto, California