Uniformly Stable Spline Approximations for Scalar Delay Problems

doi:https://doi.org/10.1007/978-1-4612-0839-6_9

Uniformly Stable Spline Approximations for Scalar Delay Problems

R.H. Fabiano-1995-01-01-Birkhäuser Boston eBooks

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TL;DRAbstract

Uniformly stable semidiscrete approximation schemes are desirable for constructing approximate solutions of certain optimal control problems for distributed parameter systems. We discuss construction of uniformly stable spline-based approximation schemes for a scalar delay equation. A method is used which employs an equivalent inner product. Convergence is established via a “hybrid” Trotter-Kato/Galerkin result.

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Uniformly stable semidiscrete approximation schemes are desirable for constructing approximate solutions of certain optimal control problems for distributed parameter systems. We discuss construction of uniformly stable spline-based approximation schemes for a scalar delay equation. A method is used which employs an equivalent inner product. Convergence is established via a “hybrid” Trotter-Kato/Galerkin result.

Keywords

Spline (mechanical)Scalar (mathematics)MathematicsGalerkin methodConvergence (economics)Applied mathematicsMathematical optimizationGeometry

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