In this article, we generalize Chebyshev＇s maximum principle to several variables. Some analogous maximum formulae for the special integration functional are given. A sufficient condition of the existence of Chebyshe...In this article, we generalize Chebyshev＇s maximum principle to several variables. Some analogous maximum formulae for the special integration functional are given. A sufficient condition of the existence of Chebyshev＇s maximum principle is also obtained.展开更多
This paper makes some mathematical analyses for the finite point method based on directional difference. By virtue of the explicit expressions of numerical formulae using only five neighboring points for computing fir...This paper makes some mathematical analyses for the finite point method based on directional difference. By virtue of the explicit expressions of numerical formulae using only five neighboring points for computing first-order and second-order directional differ- entials, a new methodology is presented to discretize the Laplacian operator defined on 2D scattered point distributions. Some sufficient conditions with very weak limitations are obtained, under which the resulted schemes are positive schemes. As a consequence, the discrete maximum principle is proved, and the first order convergent result of O（h） is achieved for the nodal solutions defined on scattered point distributions, which can be raised up to O（h2） on uniform point distributions.展开更多
基金The NSF(10826071,61033012,19201004,11271060,61272371)of China and the Fundamental Research Funds for the Central Universities
文摘In this article, we generalize Chebyshev＇s maximum principle to several variables. Some analogous maximum formulae for the special integration functional are given. A sufficient condition of the existence of Chebyshev＇s maximum principle is also obtained.
基金This project was supported by the National Natural Science Foundation of China （11371066, 11372050）, and the Foundation of National Key Laboratory of Science and Technology Computation Physics.
文摘This paper makes some mathematical analyses for the finite point method based on directional difference. By virtue of the explicit expressions of numerical formulae using only five neighboring points for computing first-order and second-order directional differ- entials, a new methodology is presented to discretize the Laplacian operator defined on 2D scattered point distributions. Some sufficient conditions with very weak limitations are obtained, under which the resulted schemes are positive schemes. As a consequence, the discrete maximum principle is proved, and the first order convergent result of O（h） is achieved for the nodal solutions defined on scattered point distributions, which can be raised up to O（h2） on uniform point distributions.
