Chapter 3 HW.xls - Numerical Solution to dy/dt = f(t,y...

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bc0cc5fe252a6e1ff226b050c30edc5db4377a4e.xls Page 1 Numerical Solution to dy/dt = f(t,y) Name f(t,y) y Exact solution (if known) Initial Conditions Initial time 0 Final time 3 Initial y value 2 Approximation Data # of subintervals 50 t (time) 0 2.000 2.000 0.06 2.120 2.120 0.12 2.247 2.247 0.18 2.382 2.382 0.24 2.525 2.525 0.3 2.676 2.676 0.36 2.837 2.837 0.42 3.007 3.007 0.48 3.188 3.188 0.54 3.379 3.379 0.6 3.582 3.582 0.66 3.797 3.797 0.72 4.024 4.024 0.78 4.266 4.266 0.84 4.522 4.522 0.9 4.793 4.793 0.96 5.081 5.081 1.02 5.386 5.386 1.08 5.709 5.709 1.14 6.051 6.051 1.2 6.414 6.414 1.26 6.799 6.799 1.32 7.207 7.207 1.38 7.639 7.639 1.44 8.098 8.098 1.5 8.584 8.584 1.56 9.099 9.099 1.62 9.645 9.645 1.68 10.223 10.223 1.74 10.837 10.837 y approx y exact y' approx Type Comments Here: 0 0.5 1 1.5 2 2.5 3 0.000 5.000 10.000 15.000 20.000 25.000 30.000 35.000 40.000 Euler Method y (ap- prox) t y
bc0cc5fe252a6e1ff226b050c30edc5db4377a4e.xls Page 2 Calculation Sheet 0 2 0 0.06 2 0 0.12 2 0 0.18 2 0 0.24 2 0 0.3 2 0 0.36 2 0 0.42 2 0 0.48 2 0 0.54 2 0 0.6 2 0 0.66 2 0 0.72 2 0 0.78 2 0 0.84 2 0 0.9 2 0 0.96 2 0 1.02 2 0 1.08 2 0 1.14 2 0 1.2 2 0 1.26 2 0 1.32 2 0 1.38 2 0 1.44 2 0 1.5 2 0 1.56 2 0 1.62 2 0 1.68 2 0 1.74 2 0 1.8 2 0 1.86 2 0 1.92 2 0 1.98 2 0 2.04 2 0 2.1 2 0 t n y n y' n t n+1/2 y n+1/2 y' n+1/2 t n y exact Euler's method : We have y n+1 = y n + h f(t n , y n) . Here h = step size = (b -a) / n and f(t n , derivative y' n at t n , since the differential equation is y ' = f(t, y). If Euler's method is select

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