In this paper, relations between directional derivatives are considered for smooth functions both in 2D and 3D spaces. These relations are established in the form of linear combinations of directional derivatives with...In this paper, relations between directional derivatives are considered for smooth functions both in 2D and 3D spaces. These relations are established in the form of linear combinations of directional derivatives with their coefficients having simple form and structural regularity. By them, expressions based on directional derivatives for some typical differential operators are derived. This builds up a solid mathematical foundation for further study on numerical computation by the finite point method based on directional difference.展开更多
Presents a study that determined a theoretical proof for the spectral analysis result of the first-order Hermite cubic spline collocation differentation matrices. Background on the Hermite cubic spline collocation met...Presents a study that determined a theoretical proof for the spectral analysis result of the first-order Hermite cubic spline collocation differentation matrices. Background on the Hermite cubic spline collocation method; Basis of the argumentation in the study regarding the condensation technique and the Hurwitz theorem; Numerical results.展开更多
Presents a study that investigated the asymptotic behavior of discrete solutions in comparison to the case of continuous solutions. Numerical representation of the problem; Details on the solution of explicit differen...Presents a study that investigated the asymptotic behavior of discrete solutions in comparison to the case of continuous solutions. Numerical representation of the problem; Details on the solution of explicit difference scheme for the corresponding nonlinear elliptic equations; Results and discussion.展开更多
基金Supported by the National Natural Science Foundation of China(No.11371066,11372050)
文摘In this paper, relations between directional derivatives are considered for smooth functions both in 2D and 3D spaces. These relations are established in the form of linear combinations of directional derivatives with their coefficients having simple form and structural regularity. By them, expressions based on directional derivatives for some typical differential operators are derived. This builds up a solid mathematical foundation for further study on numerical computation by the finite point method based on directional difference.
基金The Project supported by A Grant from the Research Grants Council of the Hong Kong Spelial Administrative Region, China (Project No. CityU 1061/00p) the Foundation of Chinese Academy of Engineering Physics.
文摘Presents a study that determined a theoretical proof for the spectral analysis result of the first-order Hermite cubic spline collocation differentation matrices. Background on the Hermite cubic spline collocation method; Basis of the argumentation in the study regarding the condensation technique and the Hurwitz theorem; Numerical results.
基金Project(Grant 10101018) Supported by National Natural Science Foundation of China.
文摘Presents a study that investigated the asymptotic behavior of discrete solutions in comparison to the case of continuous solutions. Numerical representation of the problem; Details on the solution of explicit difference scheme for the corresponding nonlinear elliptic equations; Results and discussion.
