solving ordinary differential equations fig mesh in time with corresponding discrete values (unknownsfig illustration of forward difference approximation to the derivative thirdderivatives are to be replaced by finite differences to this endwe need to know specific formulas for how derivatives can be approximated by finite differences one simple possibility is to use the definition of the derivative from any calculus booku tu td lim ! at an arbitrary mesh point tn this definition can be written as unc un ! tn lim