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The Courant-Friedrichs-Lewy condition (The CFL condition) is appeared in the analysis of the finite difference method applied to linear hyperbolic partial differential equations. We give a remark on the CFL condition from a view point of stability, and we give some numerical experiments which show instability of numerical solutions even under the CFL condition. We give a mathematical model for rounding errors in order to explain the instability.

The static second hyperpolarizabilities (γ) of open-shell organic nonlinear optical (NLO) systems composed of singlet diradical molecules are investigated using ab initio molecular orbital (MO) and density functional theory (DFT) methods. It is found that neutral singlet diradical systems with intermediate diradical characters tend to enhance γ as compared to those with small and large diradical characters. This suggests that the diradical character is a novel control parameter of γ for singlet diradical systems.

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A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE’s

Theoretical Study on Open-Shell Nonlinear Optical Systems

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A Remark on the Courant-Friedrichs-Lewy Condition in Finite Difference Approach to PDE’s

Theoretical Study on Open-Shell Nonlinear Optical Systems