Open AccessRADIAL BASIS FUNCTION METHODS FOR APPROXIMATING THE TWO-DIMENSIONAL HEAT EQUATION
Author(s) -
Tersoo Luga,
Terhemen Aboiyar,
Solomon Ortwer Adee
Publication year - 2019
Publication title -
international journal of engineering applied science and technology
Language(s) - English
Resource type - Journals
ISSN - 2455-2143
DOI - 10.33564/ijeast.2019.v04i02.002
Subject(s) - basis (linear algebra) , radial basis function , function (biology) , heat equation , mathematics , basis function , mathematical analysis , computer science , geometry , artificial intelligence , evolutionary biology , artificial neural network , biology
Radial basis function method of lines (RBFMOLs) for approximating the two-dimensional heat equation were formulated using two globally supported and positive radial basis functions (RBFs), namely, inverse quadratic (IQ), generalized inverse multiquadric (GIMQ) and the fourth order Runge-Kutta method. The RBFs were used for discretizing the space variables while the fourth order Runge-Kutta method was used as a timestepping method to integrate the resulting systems of ordinary differential equations (ODEs) that emanated from the space discretization. The methods were implemented in MATLAB and compared with the multiquadric radial basis function method of lines (MQRBF-MOLs). The performance of the proposed RBFMOLs was measured in terms of point-wise error and processing time (CPU Time). Our numerical results show that our proposed methods compared favourably with the MQ-RBF-MOLs Keywords— Radial Basis Function, Multiquadrics, Inverse Quadratics, Generalized Inverse Multiquadrics, Positive Definite RBFs, Globally Supported RBFs, Radial Basis Function Method of Lines