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Variational Approach to Stable Numerical Approximation of Optimal Dirichlet Boundary Controls for the Wave Equationстатья
- Автор: Potapov M.M.
- Сборник: Advances in Mathematics Research, Edt Albert R.Baswell
- Том: 12
- Год издания: 2012
- Место издания: Nova Science Publishers, Inc New York
- Первая страница: 95
- Последняя страница: 119
- Аннотация: This chapter considers boundary control problem for the wave equation with boundary conditions of Dirichlet type, and control actions from $L^2.$ To get numerical solutions to these problems we apply the stable variational method proposed earlier by the author. This method works well when original continuous system is controllable. Controllability property has a usual form $T>T^*$ and is supposed to be satisfied. We provide a detailed outline of the computational algorithm and give several numerical results obtained for data of varying smoothness and difference grids of varying densities. These results are compared with results of direct finite-difference approximation of initial continuous control problem via system of linear equations of high dimensionality.
- Добавил в систему: Потапов Михаил Михайлович