# Ch 5 # 15.xls - Numerical Solution to dy/dt = f(t,y Name y...

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805a849ef56e62f6590f42ef663aef0fefde6a71.xlsPage 1Numerical Solution to dy/dt = f(t,y)Namef(t,y)2*exp(-t)*yExact solution (if known)0.25*exp(2-2*exp(-t))Initial ConditionsInitial time 0Final time 15Initial y value0.25Approximation Data# of subintervals100t (time)00.2500.2500.5000.150.3300.3300.5680.30.4190.4200.6210.450.5150.5160.6570.60.6160.6160.6760.750.7170.7180.6780.90.8180.8190.6651.050.9170.9170.6411.21.0101.0110.6091.351.0991.1000.5701.51.1811.1820.5271.651.2571.2580.4831.81.3261.3270.4381.951.3891.3900.3952.11.4451.4460.3542.251.4951.4960.3152.41.5401.5410.2792.551.5791.5800.2472.71.6141.6150.2172.851.6441.6450.19031.6711.6720.1663.151.6941.6960.1453.31.7151.7160.1263.451.7321.7340.1103.61.7481.7490.0963.751.7611.7620.0833.91.7731.7740.0724.051.7831.7840.0624.21.7911.7930.0544.351.7991.8000.046yapproxyexacty'approxType Comments Here:a) as the time approaches infinity the limiting volume is exp(2)/4b) The estimate from the graph is 1.8.0246810121400.20.40.60.811.21.41.61.82Modified Euler Methody (ap-prox)y (exact)ty
CalculationPage 2Calculation Sheet00.2500.0750.25000.250.150.2500.2250.2500.150.250.30.2500.3750.2500.30.250.450.2500.5250.2500.450.250.60.2500.6750.2500.60.250.750.2500.8250.2500.750.250.90.2500.9750.2500.90.251.050.2501.1250.2501.050.251.20.2501.2750.2501.20.251.350.2501.4250.2501.350.251.50.2501.5750.2501.50.251.650.2501.7250.2501.650.251.80.2501.8750.2501.80.251.950.2502.0250.2501.950.252.10.2502.1750.2502.10.252.250.2502.3250.2502.250.252.40.2502.4750.2502.40.252.550.2502.6250.2502.550.252.70.2502.7750.2502.70.252.850.2502.9250.2502.850.2530.2503.0750.25030.253.150.2503.2250.2503.150.253.3