Diffusion models with time-dependent parameters: An analysis of computational effort and accuracy of different numerical methods

Drift-diffusion models have become valuable tools in many fields of contemporary psychology and the neurosciences. The present study compares and analyzes different methods (i.e., stochastic differential equation, integral method, Kolmogorov equations, and matrix method) to derive the first-passage time distribution predicted by these models. First, these methods are compared in their accuracy and efficiency. In particular, we address non-standard problems, for example, models with time-dependent drift rates or time-dependent thresholds. Second, a mathematical analysis and a classification of these methods is provided. Finally, we discuss their strengths and caveats.