Date of Completion
Nejat Olgac, Jiong Tang
Field of Study
Master of Science
Radial basis functions have been known for many decades, but they have not been considered for solving partial differential equations until three decades ago. Part of their attractiveness returns to the fact that without orthogonality and complicated forms of other interpolants, it is able to approximate the functions with high spectral accuracy and fast rate of convergence.
In this thesis, the relationship between polynomials and Gaussian radial basis functions is explored. Then, we use a similar approach to that of devised for polynomials to obtain a density function. Differentiation matrices are derived and shown that they estimate the function higher order derivatives with good precision.
The method for application of the boundaries is discussed after that. Finally, two systems described by PDE equations are controlled by using Linear Quadratic Controllers.
Elahidoost, Ali, "Control of Distributed Parameter Systems Using GRBF Semi-Discretization" (2012). Master's Theses. 375.