Article ID Journal Published Year Pages File Type
173893 Computers & Chemical Engineering 2008 12 Pages PDF
Abstract

The two-point boundary value problem (TPBVP) occurs in a wide variety of problems in engineering and science, including the modeling of chemical reactions, heat transfer, and diffusion, and the solution of optimal control problems. A TPBVP may have no solution, a single solution, or multiple solutions. A new strategy is presented for reliably locating all solutions of a TPBVP. The method determines narrow enclosures of all solutions that occur within a specified search interval. Key features of the method are the use of a new solver for parametric ODEs, which is used to produce guaranteed bounds on the solutions of nonlinear dynamic systems with interval-valued parameters and initial states, and the use of a constraint propagation strategy on the Taylor models used to represent the solutions of the dynamic system. Numerical experiments demonstrate the use and computational efficiency of the method.

Related Topics
Physical Sciences and Engineering Chemical Engineering Chemical Engineering (General)
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