• Journal of the Chungcheong Mathematical Society
• /
• v.9 no.1
• /
• pp.153-164
• /
• 1996

An $O(h^4)$ cubic spline collocation method for biharmonic equation with a special boundary conditions is formulated and a fast direct method is proposed for the linear system arising when the cubic spline collocation method is employed. This method requires $O(N^2\;{\log}\;N)$ arithmatic operations over an $N{\times}N$ uniform partition.

• Journal of the Korean Society for Aviation and Aeronautics
• /
• v.22 no.3
• /
• pp.74-81
• /
• 2014

The coverage area of GNSS regional ionospheric correction model is mainly determined by the disribution of GNSS ground monitoring stations. Outside the coverage area, GNSS users may receive ionospheric correction signals but the correction does not contain valid correction information. Extrapolation of the correction information can extend the coverage area to some extent. Three interpolation methods, Kriging, biharmonic spline and cubic spline, are tested to evaluate the extrapolation accuracy of the ionospheric delay corrections outside the correction coverage area. IGS (International GNSS Service) ionosphere map data is used to simulate the corrections and to compute the extrapolation error statistics. Among the three methods, biharmonic method yields the best accuracy. The estimation error has a high value during Spring and Fall. The error has a high value in South and East sides and has a low value in North side.

• International Journal of Aeronautical and Space Sciences
• /
• v.17 no.1
• /
• pp.64-72
• /
• 2016

The coverage area of a GNSS regional ionospheric delay model is mainly determined by the distribution of GNSS ground monitoring stations. Extrapolation of the ionospheric model data can extend the coverage area. An extrapolation algorithm, which combines observed ionospheric delay with the environmental parameters, is proposed. Neural network and least square regression algorithms are developed to utilize the combined input data. The bi-harmonic spline method is also tested for comparison. The IGS ionosphere map data is used to simulate the delays and to compute the extrapolation error statistics. The neural network method outperforms the other methods and demonstrates a high extrapolation accuracy. In order to determine the directional characteristics, the estimation error is classified into four direction components. The South extrapolation area yields the largest estimation error followed by North area, which yields the second-largest error.