More accurate results for two-dimensional heat equation with Neumann's and non-classical boundary conditions. (October 2016)

• Record Type: Journal Article
• Authors: Shivanian, Elyas
• Is Part Of: Engineering with computers. Volume 32:Number 4(2016)
• Page Start: 729
• Page End: 743
• Publication Date: 2016-10
• Subjects: Spectral meshless radial point interpolation (SMRPI) -- Radial basis function -- MLPG method -- Method of approximate particular solution (MAPS) -- Neumann's boundary conditions -- Non-classical integral boundary condition -- Finite differences; Engineering design -- Data processing -- Periodicals; Computer-aided design -- Periodicals; Conception technique -- Informatique -- Périodiques; Conception assistée par ordinateur -- Périodiques; Electronic journals; 620.00285
• DOI: 10.1007/s00366-016-0449-y
• Languages: English
• ISSNs: 0177-0667

Abstract

Abstract In this article, recently proposed spectral meshless radial point interpolation (SMRPI) method is applied to the two-dimensional diffusion equation with a mixed group of Dirichlet's and Neumann's and non-classical boundary conditions. The present method is based on meshless methods and benefits from spectral collocation ideas. The point interpolation method with the help of radial basis functions is proposed to construct shape functions which have Kronecker delta function property. Evaluation of high-order derivatives is possible by constructing and using operational matrices. The computational cost of the method is modest due to using strong form equation and collocation approach. A comparison study of the efficiency and accuracy of the present method and other meshless methods is given by applying on mentioned diffusion equation. Stability and convergence of this meshless approach are discussed and theoretically proven. Convergence studies in the numerical examples show that SMRPI method possesses excellent rates of convergence.