Math 209 CH3 19b.xls - Numerical Solution to dy/dt = f(t,y...

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a042b3cd4bf555285aa64735450f0168624a9afb.xls Page 1 Numerical Solution to dy/dt = f(t,y) Name Sanjana Ahmed 19b f(t,y) y*sin(t) Exact solution (if known) 2.7183*exp(-cos(t)) Initial Conditions Initial time 0 Final time 20 Initial y value 1 Approximation Data # of subintervals 200 t (time) 0 1.000 1.000 0.000 0.1 1.005 1.005 0.100 0.2 1.020 1.020 0.203 0.3 1.046 1.046 0.309 0.4 1.082 1.082 0.421 0.5 1.130 1.130 0.542 0.6 1.190 1.191 0.672 0.7 1.264 1.265 0.815 0.8 1.353 1.354 0.971 0.9 1.459 1.460 1.143 1 1.582 1.584 1.331 1.1 1.725 1.727 1.537 1.2 1.890 1.892 1.761 1.3 2.077 2.080 2.002 1.4 2.290 2.293 2.256 1.5 2.528 2.533 2.522 1.6 2.794 2.799 2.792 1.7 3.086 3.092 3.060 1.8 3.405 3.412 3.316 1.9 3.748 3.756 3.547 2 4.113 4.121 3.740 2.1 4.494 4.503 3.879 2.2 4.886 4.896 3.951 2.3 5.282 5.292 3.939 2.4 5.672 5.683 3.831 2.5 6.046 6.057 3.618 2.6 6.393 6.404 3.296 2.7 6.703 6.713 2.865 2.8 6.964 6.974 2.333 2.9 7.167 7.178 1.715 y approx y exact y' approx Type Comments Here: b) Modified Euler's Method, (n, y(20)) y(20) exact = 1.807 (50, 1.806) (100, 1.803) (200, 1.806) I am satisfied with the fit of the graphs using n=200. 0 2 4 6 8 10 12 14 16 18 20 0 1 2 3 4 5 6 7 8 Modified Euler Method y (ap- prox) y (exact) t y
Calculation Page 2 Calculation Sheet 0 1 0 0.05 1 0 0 1.000007 0.1 1 0 0.15 1 0 0.1 1.000007 0.2 1 0 0.25 1 0 0.2 1.000007 0.3 1 0 0.35 1 0 0.3 1.000007 0.4 1 0 0.45 1 0 0.4 1.000007 0.5 1 0 0.55 1 0 0.5 1.000007 0.6 1 0 0.65 1 0 0.6 1.000007 0.7 1 0 0.75 1 0 0.7 1.000007 0.8 1 0 0.85 1 0 0.8 1.000007 0.9 1 0 0.95 1 0 0.9 1.000007 1 1 0 1.05 1 0 1 1.000007 1.1 1 0 1.15 1 0 1.1 1.000007 1.2 1 0 1.25 1 0 1.2 1.000007 1.3 1 0 1.35 1 0 1.3 1.000007 1.4 1 0 1.45 1 0 1.4 1.000007 1.5 1 0 1.55 1 0 1.5 1.000007 1.6 1 0 1.65 1 0 1.6 1.000007 1.7 1 0 1.75 1 0 1.7 1.000007 1.8 1 0 1.85 1 0 1.8 1.000007 1.9 1 0 1.95 1 0 1.9 1.000007 2 1 0 2.05 1 0 2 1.000007

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