期刊
ENGINEERING WITH COMPUTERS
卷 37, 期 4, 页码 3605-3613出版社
SPRINGER
DOI: 10.1007/s00366-020-01020-z
关键词
Diffusion equation; Radial basis function; Meshless radial point Hermite interpolation; Radial point interpolation; Direct and inverse; Shape function
This paper introduces an effective technique called MRPHI for solving partial differential equations with Neumann boundary condition by utilizing radial point interpolation and Hermite-type interpolation techniques. The method is tested on various two-dimensional diffusion equations to demonstrate stability across different arbitrary domains over time.
In this paper, we propose an effective method to solve partial differential equations dependent on time with Neumann boundary condition, by examining its effectivity on direct and inverse reaction-diffusion equation. This method merges the radial point interpolation and the Hermite-type interpolation techniques to provide us suitable tools to impose the boundary condition. This technique is called meshless radial point Hermite interpolation MRPHI which utilizes the radial basis function and its derivative to prepare suitable shape functions that are the key for expanding the high-order derivative. This procedure is tested on some types of two-dimensional diffusion equations to show stability through the time in different arbitrary domains.
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