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Stiffness and mass matrices are numerically integrated over the domain of the basis plate by using Guassian quadrature.
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Waveguide directional couplers, formed by two closely spaced linear defect waveguides in a two-dimensional photonic crystal of air holes in a semiconductor matrix, are numerically studied using plane wave expansion and finite difference time domain methods.
I should mention that when a set of diffeqs uses the derivimplicit method, the full (not sparse) jacobian matrix is numerically computed.
53 to 55 are computed exactly and the local Jacobian matrix is constructed in an analytical way, while the global Jacobian matrix is numerically evaluated based on the finite difference method.
Moreover, the stability and stabilization results are formulated in form of matrix inequalities that are numerically feasible.
It is shown that the conditions of existence of an observer-based feedback can be split into a set of linear matrix inequalities that are numerically tractable.
The element stiffness and mass matrices are computed numerically by employing 3×3 Gauss Legendre product rules.
By elaborating on the Lanczos approach we also propose an alternative algorithm using elementary matrices which is numerically stable.
The space derivatives are numerically approximated by means of differentiation matrices.
The two coasts are numerically underrepresented.
Donor files are numerically coded to assure confidentiality.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com