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The local Kansa’s method for solving Berger equation. (English) Zbl 1403.65180

Summary: 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.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65D05 Numerical interpolation
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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