 However, time steps which are too large may create instabilities and affect the data quality.The von Neumann and Courant-Friedrichs-Lewy criteria are often evaluated to determine the numerical model stability.For example, consider the ordinary differential equation
The Euler method for solving this equation uses the finite difference quotient
to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get
The last equation is a finite-difference equation, and solving this equation gives an approximate solution to the differential equation.