Predicting foreign currency exchange rates using the numerical solution of the incompressible Navier–Stokes equations

The movement of exchange rates has similarities with physical phenomena, especially the movement of fluid in turbulence. The parameters change of the data information on the foreign exchange market will result in unstable exchange rates movement. These are according to changes in energy in the turbulence flow resulting in fluid particles moving randomly at fluctuating velocity. This study will predict the exchange rates of the United States Dollar (USD) to Indonesian Rupiah (IDR) using the incompressible Navier–Stokes equations which have been modified with economic parameters. The analogy of economic parameters to physical parameters such as Gross Domestic Product (GDP) as the distance between the two measured velocity points, the trade balance of two countries as fluid viscosity, and fluid flow velocity as exchange rate changes, while the inflation rates and interest rates are external forces. The numerical solution of the Navier–Stokes equations is solved using the Crank–Nicolson finite difference method. The results of the prediction of the exchange rate of USD to IDR are compared with actual exchange rate data. The exchange rate prediction results of the Navier–Stokes equations that calculated using the Crank–Nicolson scheme for one year produce an error percentage below 2.5 % of the actual exchange rate data.