ABSTRACT
Difference formulas can be derived from direct fit polynomials by fitting a polynomial to a set of symbolic data and differentiating the resulting polynomial. The truncation errors of such difference formulas can be obtained by substituting Taylor series into the difference formulas to recover the derivative being approximated accompanied by all of the neglected terms in the approximation. Use the symbolic Table 2, where Ax is considered constant, to work the following problems. Note that the algebra is simplified considerably by letting the base point value of x be zero and the other values of x be multiples of the constant increment size Ax. Table 2. Symbolic Values ofI(x)
6. Derive difference formulas for f'ex) by direct polynomial fit using the following data points: (a) i and i + 1, (b) i-I and i, (c) i-I and i + 1, (d) i-I, i, and i + I, (e) i, i + 1, and i + 2, and (f) i - 2, i-I, i, i + 1, and i + 2.
