PROMETHEE technique to select the best radial basis functions for solving the 2-dimensional heat equations based on Hermite interpolation. (January 2015)

• Record Type: Journal Article
• Authors: Kazem, Saeed; Hadinejad, Farhad
• Is Part Of: Engineering analysis with boundary elements. Volume 50(2015:Jan.)
• Page Start: 29
• Page End: 38
• Publication Date: 2015-01
• Subjects: Multiple criteria decision making -- Radial basis functions -- PROMETHEE -- Hermite interpolation -- Optimal selecting; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2014.06.009
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this work, we have decided to select the best radial basis functions for solving the 2-dimensional heat equations by applying the multiple criteria decision making (MCDM) techniques. Radial basis functions (RBFs) based on the Hermite interpolation have been utilized to approximate the solution of heat equation by using the collocation method. Seven RBFs, Gaussian (GA), Multiquadrics (MQ), Inverse multiquadrics (IMQ), Inverse quadrics (IQ), third power of Multiquadrics (MQ 3 ), Conical splines (CS) and Thin plate Splines (TPS), have been applied as basis functions as well. In addition, by choosing these functions as alternatives and calculating the error, condition number of interpolation matrix, RAM memory and CPU time, obtained by Maple software, as criteria, rating of cases with the help of PROMETHEE technique has been investigated. In the end, the best function has been selected according to the rankings.