The computation time required for modeling the nonlinear response of an axon to an applied electric field is a significant limitation to optimizing a large number of neural interface design parameters through use of advanced computer algorithms. This paper introduces two methods of predicting axon activation that incorporate a threshold that includes the magnitude of the extracellular potential to achieve increased accuracy over previous computationally efficient methods. Each method uses a modified driving function that includes the second spatial difference of the applied extracellular voltage to predict the electrical excitation of a nerve. The first method uses the second spatial difference taken at a single node of Ranvier, while the second uses a weighted sum of the second spatial differences taken at all nodes of Ranvier. This study quantifies prediction accuracy for cases with single and multiple point source stimulating electrodes. While both new methods address the major criticism of linearized prediction models, the weighted sum method provides the most robust response across single and multiple point sources. These methods improve prediction of axon activation based on properties of the applied field in a computationally efficient manner.