Math 209 CH5 15b.xls - Numerical Solution to dy/dt = f(t,y...

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bc5ed9cf40c69f89096910a5c077dff048d08105.xls Page 1 Numerical Solution to dy/dt = f(t,y) Name Sanjana Ahmed Ch. 5 f(t,y) 2*(exp(-t))*y Exact solution (if known) 1.85*(exp(-2*(exp(-t)))) Initial Conditions Initial time 0 Final time 10 Initial y value 0.25 Approximation Data # of subintervals 800 t (time) 0 0.250 0.250 0.500 0.0125 0.256 0.257 0.506 0.025 0.263 0.263 0.512 0.0375 0.269 0.269 0.518 0.05 0.276 0.276 0.524 0.0625 0.282 0.283 0.530 0.075 0.289 0.289 0.536 0.0875 0.296 0.296 0.542 0.1 0.302 0.303 0.547 0.1125 0.309 0.310 0.553 0.125 0.316 0.317 0.558 0.1375 0.323 0.324 0.563 0.15 0.330 0.331 0.569 0.1625 0.337 0.338 0.574 0.175 0.345 0.345 0.579 0.1875 0.352 0.352 0.583 0.2 0.359 0.360 0.588 0.2125 0.367 0.367 0.593 0.225 0.374 0.375 0.597 0.2375 0.382 0.382 0.602 0.25 0.389 0.390 0.606 0.2625 0.397 0.397 0.610 0.275 0.404 0.405 0.614 0.2875 0.412 0.413 0.618 0.3 0.420 0.420 0.622 0.3125 0.428 0.428 0.626 0.325 0.435 0.436 0.629 0.3375 0.443 0.444 0.633 0.35 0.451 0.452 0.636 0.3625 0.459 0.460 0.639 y approx y exact y' approx Type Comments Here: Problem #15b I increased the final time to 10 to perfectly see the equation approach and level out at approximately 1.85. As t increases, the tumor volume approaches 1.847 according to Modified Euler Method and 1.850 according to the exact equation. 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Modified Euler Method y (ap- prox) y (exact) t y
Calculation Page 2 Calculation Sheet 0 0.25 0 0.00625 0.25 0 0 0.25037 0.0125 0.25 0 0.01875 0.25 0 0.0125 0.25037 0.025 0.25 0 0.03125 0.25 0 0.025 0.25037 0.0375 0.25 0 0.04375 0.25 0 0.0375 0.25037 0.05 0.25 0 0.05625 0.25 0 0.05 0.25037 0.0625 0.25 0 0.06875 0.25 0 0.0625 0.25037 0.075 0.25 0 0.08125 0.25 0 0.075 0.25037 0.0875 0.25 0 0.09375 0.25 0 0.0875 0.25037 0.1 0.25 0 0.10625 0.25 0 0.1 0.25037 0.1125 0.25 0 0.11875

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