The local Kansa׳s method for solving Berger equation

In this paper, we present the local Kansa׳s method using radial basis functions (RBFs) to solve Berger equation which is a fourth order partial differential equation. To overcome the difficulty of solving higher order differential equations using localized RBF methods, we split the given equation into two second order partial differential equations. Furthermore, we use Matern function and normalized MQ as basis functions and make a comparison between the two radial basis functions in terms of accuracy and stability. LOOCV (Leave-One-Out-Cross-Validation) is used to find a good shape parameter of MQ and Matern function. To demonstrate the effectiveness of the local Kansa׳s method for solving Berger equation, three examples are given.