Question

ME/AE 342 - Numerical Methods in Engineering with Applications Homework 2 1. Use finite difference approximation to compute f'(2.36), /'(2.37) and /"(2.37) from the data 2.36 2.37 2.38 2 .39 0.85866 0.86289 0.86710 0.87129 1() 2. Estimate f'(1) from the following data using either forward or backward dif- ference 1 f(0) 0 .97 0.85040 1.00 1.05 0.84147 0.82612 3. Use polynomial interpolation to compute f' and l" at r = 0, using the data be- low. Hint: Find the Lagrange polynomial and differentiate it to get the deriva- lives. Then calculate their values at x = 0. -2.2 1x) 15.180 -0.3 0.8 1.9 10.962 1.920 -2.010

Answer 1

" The finite difference table for the green data a y =fcw) by Y my sy 12.36 0.85866 ay 0.00423 9.37 0.86289 ay. -0.00002 2.38 0.00421 0.86710 0.87129 -0.00002 0.00419 2.39 from Newton's forward interpolation 1.2.36 00 P=0 001 f(026)= =[ 14-447+464 -4 047 --] - ob [sentent - 4 (-0.00002) –o) - [ 0.00423 +0.0000) +2:36) = 0.424 f'(2.33) = 04+1 84o đ0%*------] - 0.00423 +į (-0.00002)-0---) esto (0-00423 – 0.00001] - 0.00422 0-0) of (2.37) = 0.422 + " CP:32) = Pa = 114 + 44+--) - oba -0.00002] =|-0-22 00