In this paper, we propose the Laguerre spectral method for high order problems with mixed inhomogeneous boundary conditions. It is also available for approximated solutions growing fast at infinity. The spectral accuracy is proved. Numerical results demonstrate its high effectiveness.

We propose a collocation method for solving initial value problems of second-order ODEs by using modified Laguerre functions. This new process provides global numerical solutions. Numerical results demonstrate the efficiency of the proposed algorithm.

SrBi2Ta2O9 (SBT) films were prepared on Pt/TiO2/SiO2/Si substrates at 750 °C in oxygen by the metalorganic decomposition method. SBT film capacitors were postannealed in Ar (N2) at 350–750 °C and then reannealed in O2 at 750 °C. Effects of annealing atmosphere on the structure, morphology, and ferroelectric properties have been investigated systematically. The composition analyses indicate Ar- or N2-annealing at 750 °C leads to Bi evaporation and oxygen loss. Above 550 °C 100% Ar or N2 postannealing, the remnant polarization decreases and the coercive field increases significantly. The subsequent O2 recovery can hardly rejuvenate the electrical properties. The result is different from that with the effective O2 recovery in forming gas processing (annealing in an atmosphere containing 5% hydrogen). The possible origin and mechanism is discussed and proposed.

Hermite polynomial interpolation is investigated. Some approximation results are obtained. As an example, the Burgers equation on the whole line is considered. The stability and the convergence of proposed Hermite pseudospectral scheme are proved strictly. Numerical results are presented.

The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is proposed, which is easy to be performed. The numerical solution possesses the accuracy of second-order in time and higher order in space. The numerical experiments show the high accuracy of this approach.