Over the past decade, the blockchain technology and its bitcoin cryptocurrency have received considerable attention. Bitcoin has experienced significant price swings in daily and long-term valuations. In this paper, we propose a partial differential equation (PDE) model on the bitcoin transaction network for forecasting the bitcoin price movement. Through analysis of bitcoin subgraphs or chainlets, the PDE model captures the influence of transaction patterns on the bitcoin price over time and combines the effect of all chainlet clusters. In addition, Google Trends index is incorporated to the PDE model to reflect the effect of the bitcoin market sentiment. The experiment results demonstrate that the PDE model is capable of forecasting the bitcoin price movement. The paper is the first attempt to apply a PDE model to the bitcoin transaction network for forecasting.