ABSTRACT
In problems of engineering interest, the numerical solution is generally based on discrete values of a given function and its derivatives at a ˜nite number of points in the computational domain. The need to discretize a function arises since a digital computer can usually carry out only the standard arithmetic operations, employing a ˜nite number of discrete values. Also, in many cases, interest lies in estimating the derivatives from discrete numerical or experimental values of the function, given at speci˜ed data points. The derivatives are then computed at these data points or at a number of intermediate locations, employing only arithmetic operations. Similarly, the numerical integration of a function may be carried out, using the discrete values of the function. Of course, as mentioned earlier, symbolic algebra may also be used in a few limited cases to differentiate or integrate continuous functions, employing software such as Maple or Mathematica. This chapter discusses the basic concepts involved in discretization as well as in the computation of the derivatives of a given function from given discrete values.
