Abstract. In a foregoing paper [Sonar, ESAIM: M2AN 39 (2005) 883-908] we analyzed the Interpolating Moving Least Squares (IMLS) method due to Lancaster andŠalkauskas with respect to its approximation powers and derived finite difference expressions for the derivatives. In this sequel we follow a completely different approach to the IMLS method given by Kunle [Dissertation (2001)]. As a typical problem with IMLS method we address the question of getting admissible results at the boundary by introducing "ghost points". Most interesting in IMLS methods are the finite difference operators which can be computed from different choices of basis functions and weight functions. We present a way of deriving these discrete operators in the spatially one-dimensional case. Multidimensional operators can be constructed by simply extending our approach to higher dimensions. Numerical results ranging from 1-d interpolation to the solution of PDEs are given.Mathematics Subject Classification. 65M06, 65M60, 65F05.
This project aims to study the factors causing moisture migration and moisture loss of grain in storage grain that subsequently affect production costs by compensating lost weight due to its moisture. From reviewing a related mathematical model, it is found that physical changes of grain in silo, both the temperature and moisture, are caused by its oxidation during storage and aeration. Therefore, suitable grain storage can reduce its weight loss. To control storing process, the numerical solution of the model, a system of partial differential equations, is obtained by finite difference method. Moreover, a Java program has developed based on overall processes of the model as an information for decision making in grain production and storage.
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