Ch 5 # 11.xls - Numerical Solution to dy/dt = f(t,y Name y...

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8b08e816a35200643bef36d883b5253d4bd96632.xls Page 1 Numerical Solution to dy/dt = f(t,y) Name f(t,y) (.0315*y)*(1-(y/189)) Exact solution (if known) Initial Conditions Initial time 0 Final time 150 Initial y value 3.929 Approximation Data # of subintervals 6400 t (time) 0 3.929 0.121 0.0234375 3.932 0.121 0.046875 3.935 0.121 0.0703125 3.938 0.121 0.09375 3.940 0.122 0.1171875 3.943 0.122 0.140625 3.946 0.122 0.1640625 3.949 0.122 0.1875 3.952 0.122 0.2109375 3.955 0.122 0.234375 3.958 0.122 0.2578125 3.960 0.122 0.28125 3.963 0.122 0.3046875 3.966 0.122 0.328125 3.969 0.122 0.3515625 3.972 0.122 0.375 3.975 0.123 0.3984375 3.978 0.123 0.421875 3.980 0.123 0.4453125 3.983 0.123 0.46875 3.986 0.123 0.4921875 3.989 0.123 0.515625 3.992 0.123 0.5390625 3.995 0.123 0.5625 3.998 0.123 0.5859375 4.001 0.123 0.609375 4.004 0.123 0.6328125 4.006 0.124 0.65625 4.009 0.124 0.6796875 4.012 0.124 y approx y exact y' approx Type Comments Here: Note: 1790 ----> t initial which t = 0 Approx. Actual (Equation) (Census) 1800 (t= 10) 5.344 5.308 1810 (t=20) 7.248 7.239 1820( t=30) 9.789 9.638 1830 (t=40) 13.163 12.866 1840 (t=50) 17.588 17.069 1850 (t=60) 23.287 23.192 1860 (t=70) 30.524 31.443 1870 (t=80) 39.473 39.818 1880 (t=90) 50.188 50.156 1890 (t=100) 62.445 62.948 1900 (t=110) 76.512 75.995 1910 (t=120) 91.083 91.973 1920 (t=130) 105.921 105.711 1930 (t=140) 120.208 122.775 1940 (t=150) 133.301 131.669 0 20 40 60 80 100 120 140 0.000 20.000 40.000 60.000 80.000 100.000 120.000 140.000 Modified Euler Method t y
Calculation Page 2 Calculation Sheet 0 3.929 0 0.011719 3.929 0 0.023438 3.929 0 0.035156 3.929 0 0.046875 3.929 0 0.058594 3.929 0 0.070313 3.929 0 0.082031 3.929 0 0.09375 3.929 0 0.105469 3.929 0 0.117188 3.929 0 0.128906 3.929 0 0.140625 3.929 0 0.152344 3.929 0 0.164063 3.929 0 0.175781 3.929 0 0.1875 3.929 0 0.199219 3.929 0 0.210938 3.929 0 0.222656 3.929 0 0.234375 3.929 0 0.246094 3.929 0 0.257813 3.929 0 0.269531 3.929 0 0.28125 3.929 0 0.292969 3.929 0 0.304688 3.929 0 0.316406 3.929 0 0.328125 3.929 0 0.339844 3.929 0 0.351563 3.929 0 0.363281 3.929 0 0.375 3.929 0 0.386719 3.929 0 0.398438 3.929 0 0.410156 3.929 0 0.421875 3.929 0 0.433594 3.929 0 0.445313 3.929 0 0.457031 3.929 0 0.46875 3.929 0 0.480469 3.929 0 0.492188 3.929 0 0.503906 3.929 0 0.515625 3.929 0 0.527344 3.929 0 0.539063 3.929 0 0.550781 3.929 0 0.5625 3.929 0 0.574219 3.929 0 0.585938 3.929 0 0.597656 3.929 0 0.609375 3.929 0 0.621094 3.929 0 0.632813 3.929 0 0.644531 3.929 0 0.65625 3.929 0 0.667969 3.929 0 0.679688 3.929 0 0.691406 3.929 0 0.703125 3.929 0 0.714844 3.929 0 0.726563 3.929 0 0.738281 3.929 0 0.75 3.929 0 0.761719

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