Under the architecture of a neural network, this work proposes and applies three multiquadric radial basis function (MQ-RBF) interpolation schemes; The Common Local Radial Basis Function Scheme (CLRBF), The Iterative Local Radial Basis Function Scheme (ILRBF), and The Radius Local Radial Basis Function Scheme (RLRBF). The schemes are designed to perform locally to overcome drawbacks normally encountered when using a global one. The famous Franke function in two dimensions is numerically tackled. It is revealed in this work that all three local methods outperform the traditional MQ interpolation in terms of both CPU-time and condition number, while the accuracy is overall acceptable, particularly when the number of nodes increases. This finding indicates their potential for dealing with bigger datasets and more complex problems.