Problem 2. Newton's Interpolation Methods
The following table gives the longitude of the moon at twelve-hour intervals for the first four days of April, 1918. Find the moon's longitude at 8:50 PM on April 2, 1918, using Newton's interpolation methods.
Date Time Moon's Longitude April 1, 1918 0 244o 44' 20.5'' April 1, 1918 12 250o 57' 35.7'' April 2, 1918 0 257o 14' 22.1'' April 2, 1918 12 263o 35' 08.6'' April 3, 1918 0 270o 00' 24.6'' April 3, 1918 12 276o 30' 39.6'' April 4, 1918 0 283o 06' 22.1''
Done. See Interpolation.htm
Problem 3. Stirling's Interpolation Method
Using Stirling's formula, compute the value of (2/p1/2) o/x (e-x2) dx, when x = 0.6538, given the following table (where o/x represents a definite integral sign).
x (2/p1/2) o/x (e-x2) dx 0.62 0.6194114 0.63 0.6270463 0.64 0.6345857 0.65 0.6420292 0.66 0.6493765 0.67 0.6566275 0.68 0.6637820
Done. See Interpolation.htm
Problem 4. Lagrangian Interpolation
The following table gives certain corresponding values of x and log10x. Using Lagrangian interpolation, compute the value of log10(323.5).
x log10x 321.0 2.50651 322.8 2.50893 324.2 2.51081 325.0 2.51188
Done. See Interpolation.htm