The line method is used to discretize partial differential
equations transforming the original
system into a system of ordinary differential equations.
Discretized differential equations and coupled ordinary differential
or differential algebraic equations are solved by standard explicit or
implicit integration methods.
Thus, the optimal control problem is transformed into a nonlinear programming problem which is solved by a sequential quadratic programming method. Time-dependent inequality constraints are discretized w.r.t. given break points.
We outline the mathematical formulation of the optimal control problem that can be solved numerically by PDECON, describe the program organisation and usage, and present a couple of examples, most of them with some practical background. Especially we show how to solve a control problem where the diffusion of a substance through the skin is controlled by an external electrical field.
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