Constructing the weighting coefficients for the RBF-Hermite FD scheme under the multiquadric function on irregular meshes

It is well known that the order of finite difference estimates on nonuniform grids reduce dramatically, particularly when higher order derivatives are required. This paper contributes how an optimization of the order of approximation formulas can be investigated and done on such grids for a sufficiently smooth function. To generalize the idea as well as get the optimized orders, the notion of radial basis function-Hermite finite difference (RBF-HFD) approach is used. The new weighting coefficients are worked out and proved to possess higher convergence rates. Several tests are also given to demonstrate the theoretical discussions.

Automated summary

This paper investigates and optimizes the order of approximation formulas on nonuniform grids using the RBF-HFD approach, resulting in new weighting coefficients with higher convergence rates. Theoretical discussions are supported with several tests to demonstrate the effectiveness of the method.