Ahmad Shirzadi

The radial basis functions are commonly used to solve the partial differential equations. The simplicity of these functions in numerical implementation for problems with complex computational domains and high dimension, as well as the high accuracy of approximation of these functions, has made them become a useful tool in engineering sciences. In this thesis, a numerical method for solving the spacial dependent heat inverse problem has been investigated using radial basis functions. The purpose of writing this thesis is to correct the error that occurred in an article titled ”A radial basis function collocation method for space-dependent inverse heat problems”, published in ”Journal of Applied and Computational Mechanics ” journal (2020) [1] which has invalidated the numerical results of that article. Therefore, a numerical method for solving the inverse heat problem using the collocation method of Gaussian radial basis functions and inverse multiquadric in one spatial dimension is considered. In order to evaluate this method, extensive numerical experiments have been conducted, including the study of the effect of the shape parameter, arrangement of the collocation points, and the types of radial basis functions on the numerical solutions. Also, in some cases, the numerical results obtained using the collocation method have been compared with the finite difference method. The numerical results show the effectiveness of radial basis functions for problem solving.