Multidimensional interpolation using osculatory radial basis functions

A procedure has been developed for the interpolation of functions defined in two dimensions using the values of the function and its normal derivatives at the boundary. The interpolating functions used are combinations of two classes of radial basis functions. This permits an interpolation scheme with osculatory features, i.e., the interpolant has a specified slope at the boundary interpolation points. The improved accuracy of the method is demonstrated over interpolation schemes using the traditional radial basis functions (with no osculation), especially for the calculation of the derivatives of the function at various internal points. A brief discussion on the utility of the new interpolation technique in solving nonlinear Poisson problems using the dual reciprocity boundary element method is provided.