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Consider the five-point finite difference grid illustrated in Figure 8.19. Fourth-order approximations for ji' and ji" require five grid points: i - 2 to i + 2. The sixth-order Taylor series for y(x) at these points with base point i are given by

- - -'1(2 A--) l-III(2A--)2 l-IIII(2A--)3 l-iv l(2 A__)4Yi+2 = Yi +Y i L.U + 2:Y i L.U + ilY i L.U + MY i L.U + lio7li(2 Ax)5 + 7io7 i li(2 Ax)6 + ...