Random variable shape parameter strategy to minimize error in Oscillatory radial basis function approximation method for solving partial differential equations.

Approximation of the functions which are the solutions of complex or difficult problems is a worthwhile endeavor. This has resulted in many ways to effectively approximate the solution of the partial differential equations. One such way to approximate the solution of the partial differential equation is Oscillatory radial basis function method. This method can approximate the solution of the partial differential equation well however relies heavily on a “shape parameter” to achieve acceptable error. Choosing this parameter was traditionally done through a trial-and-error method. Selecting shape parameters in a more analytical way has been desired. One such method is the Random variable shape parameter strategy, where the shape parameter is randomly chosen in a predefined interval. This method has been shown to be effective when coupled with other radial basis functions methods. This work is concerned with testing the efficacy of random variable shape parameter strategy when using an oscillatory radial basis function for solving a variety of partial differential equations