Exercises_3pt14_pt15_4pt2.xlsm - Joseph John 6-Feb-18 3.14...

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Joseph, John 6-Feb-18 3.14. 1000 3.15.a. DELTA_T P DELTA_T*P % Rounding Error (using VBA code) 0.4 1000000 403833.375 0.95834375 0.4 2000000 #VALUE! #VALUE! 0.4 3000000 1163099.125 -3.0750729167 0.4 4000000 #VALUE! #VALUE! 0.4 5000000 #VALUE! #VALUE! 0.4 6000000 #VALUE! #VALUE! 0.4 7000000 #VALUE! #VALUE! 0.4 8000000 #VALUE! #VALUE! 0.4 9000000 #VALUE! #VALUE! 0.4 10000000 #VALUE! #VALUE! 0.5 5000000 #VALUE! #VALUE! 0.5 10000000 #VALUE! #VALUE! 0.6 1000000 #VALUE! #VALUE! 0.6 2000000 #VALUE! #VALUE! 0.6 3000000 #VALUE! #VALUE! 0.6 4000000 #VALUE! #VALUE! 0.6 5000000 #VALUE! #VALUE! 0.6 6000000 #VALUE! #VALUE! 0.6 7000000 #VALUE! #VALUE! 0.6 8000000 #VALUE! #VALUE! 0.6 9000000 #VALUE! #VALUE! 0.6 10000000 #VALUE! #VALUE! 3.15.b. % Rounding Error % Rounding Error P DELTA_T = 0.4 DELTA_T=0.6 1000000 0.96 -0.15 2000000 -1.49 2.01 3000000 -3.08 2.73 4000000 -3.87 -0.05 5000000 -4.35 -3.38 6000000 -2.01 -5.59 7000000 1.85 -7.17 8000000 4.74 -8.36 9000000 6.99 -9.28 % Rounding Error
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10000000 8.79 -10.02 3.15.c. The magnitude of the % rounding error generally increases as the number of operations incre 3.15.d. 0.5 can be represented exactly in the binary system, and sums of 0.5 can as well, until an over 3.15.e. It would be extremely difficult, maybe impossible. Even for the simple operation in the table, 4.2.b, c, d. delta_t 0.5 i t_i y_i_Euler y_i_analytical 1 0 2 2 2 0.5 2 2.0289304385 3 1 2.0575 2.1179235217 4 1.5 2.175375 2.2738661909 5 2 2.361028125 2.5092263438 6 2.5 2.6271309375 2.8437272647 7 3 2.9930223047 3.3071180266 8 3.5 3.4869756504 3.9435879369 9 4 4.1496963892 4.8187441355 10 4.5 5.0396356671 6.0306892908 11 5 6.2410536921 7.7277888022 12 5.5 7.8763171152 10.137542092 13 6 10.1248043218 13.6141891681 14 6.5 13.2522456184 18.7184416757 15 7 17.6567254444 26.3531974542 16 7.5 23.9415793499
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