| Popis: |
This chapter describes different aspects of finite-difference methods. Given a function y of x , a difference table can be constructed if y is given for equally spaced values of x . This constant interval, or step length in x is often denoted by h . The difference table is made up of columns, and the first column lists the values of x , the second column lists the corresponding values of y . The next column is the column of first differences denoted by Ay , the entries in this column being derived from the y column by differencing it. The gradual variation of consecutive entries in each column, and the way entries get smaller in absolute values for higher differences up to a certain order, beyond which they become erratic, and begin to increase again is elaborated. It is found that if the interval of tabulation is small enough, the gradual variation, and initial decrease in magnitude are characteristic of well-behaved functions, and when they do not occur it is usually because an arithmetic blunder has taken place somewhere. |
