Defeating 2-D Runge Problem by Coefficients and Order Determination (CAOD) Method

Runge problem is a problem of edge-oscillations in polynomial interpolation of Runge function at evenly spaced nodes. While many works have been presented to defeat the 1-dimensional (1-D) Runge problem, its higher dimensional cases are rarely discussed. Our previous works have presented an approximation method called CAOD method to defeat the 1-D Runge problem. In this paper, we generalize this method to defeat the 2- (or higher-) dimensional Runge problem, and conduct computer experiments to substantiate the accuracy of the method.