13a.xls - Numerical Solution of System dx/dt = f(t,x,y...

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b311de099f762fe47938aab8fb3846b5818d24b0.xls Page 1 Numerical Solution of System dx/dt = f(t,x,y), dy/dt = g(t,x,y) Name Muskan Aryal f(t,x,y) -x+.01*x*y g(t,x,y) y*(1-y/20-x/5) Initial Conditions Initial time 0 Final time 15 Initial x value 8 Initial y value 15 Approximation Data # of subintervals 100 t = 0.00 Type Comments Here: 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 16 Solution Curves x(approx) y (approx) t x, y 7 8 9 10 11 12 13 14 15 16 0 2 4 6 8 10 12 14 16 Phase Plane x y 0 2 4 6 8 10 12 14 0 5 10 15 20 25 30 Phase Portrait x y Scroll Me
Calculation Page 2 Calculation Sheet 0 8 15 0 0 0.075 8 15 0 0.15 8 15 0 0 0.225 8 15 0 0.3 8 15 0 0 0.375 8 15 0 0.45 8 15 0 0 0.525 8 15 0 0.6 8 15 0 0 0.675 8 15 0 0.75 8 15 0 0 0.825 8 15 0 0.9 8 15 0 0 0.975 8 15 0 1.05 8 15 0 0 1.125 8 15 0 1.2 8 15 0 0 1.275 8 15 0 1.35 8 15 0 0 1.425 8 15 0 1.5 8 15 0 0 1.575 8 15 0 1.65 8 15 0 0 1.725 8 15 0 1.8 8 15 0 0 1.875 8 15 0 1.95 8 15 0 0 2.025 8 15 0 2.1 8 15 0 0 2.175 8 15 0 2.25 8 15 0 0 2.325 8 15 0 2.4 8 15 0 0 2.475 8 15 0 2.55 8 15 0 0 2.625 8 15 0 2.7 8 15 0 0 2.775 8 15 0 2.85 8 15 0 0 2.925 8 15 0 3 8 15 0 0 3.075 8 15 0 3.15 8 15 0 0 3.225 8 15 0 3.3 8 15 0 0 3.375 8 15 0 3.45 8 15 0 0 3.525 8 15 0 3.6 8 15 0 0 3.675 8 15 0 3.75 8 15 0 0 3.825 8 15 0 3.9 8 15 0 0 3.975 8 15 0 4.05 8 15 0 0 4.125 8 15 0 4.2 8 15 0 0 4.275 8 15 0 4.35 8 15 0 0 4.425 8 15 0 4.5 8 15 0 0 4.575 8 15 0 4.65 8 15 0 0 4.725 8 15 0 4.8 8 15 0 0 4.875 8 15 0 4.95 8 15 0 0 5.025 8 15 0 5.1 8 15 0 0 5.175 8 15 0 5.25 8 15 0 0 5.325 8 15 0 t n x n y n x' n y' n t n+1/2 x n+1/2 y n+1/2 x' n+1/2 Calculation: The modified euler method is used to compute the successive approximations. T

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