A RBFWENO finite difference scheme for Hamilton-Jacobi equations

Abstract The aim of this paper is to study the numerical application of radial basis functions (RBFs) approximation in the reconstruction process of well known ENO/WENO schemes. The resulted schemes are employed for approximating the viscosity solution of Hamilton–Jacobi (H–J) equations. The accuracy in the smooth area is enhanced by locally optimizing the shape parameter according to the results. It is revealed that the proposed schemes in this research prepare more accurate reconstructions and sharper solution near singularities by comparing the RBFENO/RBFWENO schemes and the classical ENO/WENO schemes for some benchmark examples. Looking at the several numerical examples in 1D, 2D and 3D illustrate that the proposed schemes in this paper perform better than the traditional ENO/WENO schemes for solving H–J equations.

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