Math 209 CH4 33c.xls - Numerical Solution to dy/dt = f(t,y...

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07c15efedc4a27d98520ee1d11880c55a9986583.xlsPage 1Numerical Solution to dy/dt = f(t,y)NameSanjana Ahmed Ch. 4f(t,y)y^2Exact solution (if known)Initial ConditionsInitial time 0Final time 1Initial y value1Approximation Data# of subintervals1000t (time)01.0001.0000.0011.0011.0020.0021.0021.0040.0031.0031.0060.0041.0041.0080.0051.0051.0100.0061.0061.0120.0071.0071.0140.0081.0081.0160.0091.0091.0180.011.0101.0200.0111.0111.0220.0121.0121.0240.0131.0131.0270.0141.0141.0290.0151.0151.0310.0161.0161.0330.0171.0171.0350.0181.0181.0370.0191.0191.0390.021.0201.0410.0211.0211.0430.0221.0221.0450.0231.0241.0480.0241.0251.0500.0251.0261.0520.0261.0271.0540.0271.0281.0560.0281.0291.0580.0291.0301.061yapproxyexacty'approxType Comments Here:Problem #33cI set the number of subintervals to 1000 to properly see the blow-up phenomenon with more accurate y-values. There is a vertical asymptote slightly near t=1. 00.10.20.30.40.50.60.70.80.910.000200.000400.000600.000800.0001000.0001200.0001400.0001600.0001800.0002000.000Modified Euler Methodty
CalculationPage 2Calculation Sheet0100.0005100.001100.0015100.002100.0025100.003100.0035100.004100.0045100.005100.0055100.006100.0065100.007100.0075100.008100.0085100.009100.0095100.01100.0105100.011100.0115100.012100.0125100.013100.0135100.014100.0145100.015100.0155100.016100.0165100.017100.0175100.018100.0185100.019100.0195100.02100.0205100.021100.0215100.022100.0225100.023100.0235100.024100.0245100.025100.0255100.026100.0265100.027100.0275100.028100.0285100.029100.0295100.03100.0305100.031100.0315100.032100.0325100.033100.0335100.03410