A feature of new economic geography model is their mathematical intractability. This intractability results from the fact that the functional relationship between the indirect utility differential and the state variable cannot be found explicitly. We illustrate three methods that can be utilized to approximate the unknown function. These methods are simple and give a remarkable improvement in the precision of approximation with respect to the commonly utilized Lagrange approximation. Precision of approximation is important in models that feature catastrophic behavior. We apply these methods to the core-periphery model. Naturally, they can be applied to all cases of unknown functional relationships.