Space-time spectral collocation method for one-dimensional PDE constrained optimisation

This paper solves an optimal control problem governed by a parabolic PDE. Using Lagrangian multipliers, necessary conditions are derived and then space-time spectral collocation method is applied to discretise spatial derivatives and time derivatives. This method solves partial differential equation...

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Bibliographic Details
Published inInternational journal of control Vol. 93; no. 5; pp. 1231 - 1241
Main Authors Rezazadeh, A., Mahmoudi, M., Darehmiraki, M.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.05.2020
Taylor & Francis Ltd
Subjects
Collocation methods
Convergence
Derivatives
Exact solutions
Mathematical analysis
Optimal control
Optimization
Parabolic differential equations
parabolic equation
partial differential equation
Partial differential equations
Primary 43A62
Secondary 42C15
space-time spectral collocation method
Spectra
Spectral methods
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Summary:This paper solves an optimal control problem governed by a parabolic PDE. Using Lagrangian multipliers, necessary conditions are derived and then space-time spectral collocation method is applied to discretise spatial derivatives and time derivatives. This method solves partial differential equations numerically with errors bounded by an exponentially decaying function which is dependent on the number of modes of analytic solution. Spectral methods, which converge spectrally in both space and time, have gained a significant attention recently. The problem is then reduced to a system consisting of easily solvable algebraic equations. Numerical examples are presented to show that this formulation has exponential rates of convergence in both space and time.
ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2018.1501161