 The reduction of the differential equation to a system of algebraic equations makes the problem of finding the solution to a given ODE/PDE ideally suited to modern computers, hence the widespread use of FDMs in modern numerical analysis.Today, FDMs are the dominant approach to numerical solutions of PDEs.First, assuming the function whose derivatives are to be approximated is properly-behaved, by Taylor's theorem, we can create a Taylor series expansion

where "n"!