Radial Basis Function and Its Application for Engineering Field

An essential part of studying mathematical models in science and engineering is the study of partial differential equations. To solve differential equations, academics have created a variety of tools and methods. It has been demonstrated that radial basis functions are an effective basis function for estimating the solutions of partial and ordinary differential equations. Researchers have created a variety of radial basis function techniques to solve a number of well-known differential equations. It has been created to approximate the solution using a variety of techniques that result in the creation of hybrid methods. Because radial basis function approaches can handle meshless domains, they are frequently employed in numerical analysis and statistics. The various radial basis function approaches were examined in this work, with an emphasis on the methods being used to determine the value of the shape parameter. The possible shape parameters to obtain the optimal value of the numerical solutions are examined, as are the mathematical formulations of the various radial basis function approaches. The current effort will establish a platform for comprehending the evolution of radial basis functions, which may play a significant role in the subsequent development of the approach.