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non_lin_tut_sol1 - Non-linear Equations Non-linear...

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Non-linear Equations Non-linear Equations tutorial solutions 1 a) 2x^3+3x-3 -4 -2 0 2 4 6 8 10 0 0.5 1 1.5 2 Bisection Method fx=2x^3+3x-3 I x1 x2 xm f(xm) f(x1) f(xm)f(x1) abs(f(xm)) abs(x1-x2) 0 0 1 0.5 -1.25 -3 3.75 1.25 1 1 0.5 1 0.75 0.09375 -1.25 -0.11719 0.09375 0.5 2 0.5 0.75 0.625 -0.63672 -1.25 0.795898 0.636719 0.25 3 0.625 0.75 0.6875 -0.2876 -0.63672 0.183119 0.287598 0.125 4 0.6875 0.75 0.71875 -0.10114 -0.2876 0.029086 0.101135 0.0625 5 0.71875 0.75 0.734375 -0.00477 -0.10114 0.000482 0.004768 0.03125 6 0.734375 0.75 0.742188 0.044219 -0.00477 -0.00021 0.044219 0.015625 7 0.734375 0.742188 0.738281 0.019658 -0.00477 -9.4E-05 0.019658 0.007813 8 0.734375 0.738281 0.736328 0.007428 -0.00477 -3.5E-05 0.007428 0.003906 9 0.734375 0.736328 0.735352 0.001326 -0.00477 -6.3E-06 0.001326 0.001953 10 0.734375 0.735352 0.734863 -0.00172 -0.00477 8.21E-06 0.001722 0.000977 11 0.734863 0.735352 0.735107 -0.0002 -0.00172 3.42E-07 0.000199 0.000488 12 0.735107 0.735352 0.735229 0.000563 -0.0002 -1.1E-07 0.000563 0.000244 13 0.735107 0.735229 0.735168 0.000182 -0.0002 -3.6E-08 0.000182 0.000122 14 0.735107 0.735168 0.735138 -8.2E-06 -0.0002 1.64E-09 8.24E-06 6.1E-05 15 0.735138 0.735168 0.735153 8.7E-05 -8.2E-06 -7.2E-10 8.7E-05 3.05E-05 16 0.735138 0.735153 0.735146 3.94E-05 -8.2E-06 -3.2E-10 3.94E-05 1.53E-05 17 0.735138 0.735146 0.735142 1.56E-05 -8.2E-06 -1.3E-10 1.56E-05 7.63E-06 18 0.735138 0.735142 0.73514 3.67E-06 -8.2E-06 -3E-11 3.67E-06 3.81E-06 19 0.735138 0.73514 0.735139 -2.3E-06 -8.2E-06 1.88E-11 2.28E-06 1.91E-06 20 0.735139 0.73514 0.735139 6.92E-07 -2.3E-06 -1.6E-12 6.92E-07 9.54E-07 1
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Non-linear Equations b) cosx + x -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 Bisection Method fx=cosx + x I x1 x2 xm f(xm) f(x1) f(xm)f(x1) abs(f(xm)) abs(x1-x2) 0 -1 0 -0.5 0.377583 -0.4597 -0.17357 0.377583 1 1 -1 -0.5 -0.75 -0.01831 -0.4597 0.008418 0.018311 0.5 2 -0.75 -0.5 -0.625 0.185963 -0.01831 -0.00341 0.185963 0.25 3 -0.75 -0.625 -0.6875 0.085335 -0.01831 -0.00156 0.085335 0.125 4 -0.75 -0.6875 -0.71875 0.033879 -0.01831 -0.00062 0.033879 0.0625 5 -0.75 -0.71875 -0.73438 0.007875 -0.01831 -0.00014 0.007875 0.03125 6 -0.75 -0.73438 -0.74219 -0.0052 -0.01831 9.51E-05 0.005196 0.015625 7 -0.74219 -0.73438 -0.73828 0.001345 -0.0052 -7E-06 0.001345 0.007813 8 -0.74219 -0.73828 -0.74023 -0.00192 -0.0052 1E-05 0.001924 0.003906 9 -0.74023 -0.73828 -0.73926 -0.00029 -0.00192 5.56E-07 0.000289
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