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

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62d24e6dc777acc7c2028916d7aa0bf24dce211d.xls Page 1 Numerical Solution of System dx/dt = f(t,x,y), dy/dt = g(t,x,y) Name f(t,x,y) -x+0.1*x*y g(t,x,y) y-.2*x*y Initial Conditions Initial time 0 Final time 15 Initial x value 2 Initial y value 4 Approximation Data # of subintervals 100 t = 0.00 Type Comments Here: 0 2 4 6 8 10 12 14 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Solution Curves x(approx) y (approx) t x, y 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 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 2 4 0 0 0.075 2 4 0 0.15 2 4 0 0 0.225 2 4 0 0.3 2 4 0 0 0.375 2 4 0 0.45 2 4 0 0 0.525 2 4 0 0.6 2 4 0 0 0.675 2 4 0 0.75 2 4 0 0 0.825 2 4 0 0.9 2 4 0 0 0.975 2 4 0 1.05 2 4 0 0 1.125 2 4 0 1.2 2 4 0 0 1.275 2 4 0 1.35 2 4 0 0 1.425 2 4 0 1.5 2 4 0 0 1.575 2 4 0 1.65 2 4 0 0 1.725 2 4 0 1.8 2 4 0 0 1.875 2 4 0 1.95 2 4 0 0 2.025 2 4 0 2.1 2 4 0 0 2.175 2 4 0 2.25 2 4 0 0 2.325 2 4 0 2.4 2 4 0 0 2.475 2 4 0 2.55 2 4 0 0 2.625 2 4 0 2.7 2 4 0 0 2.775 2 4 0 2.85 2 4 0 0 2.925 2 4 0 3 2 4 0 0 3.075 2 4 0 3.15 2 4 0 0 3.225 2 4 0 3.3 2 4 0 0 3.375 2 4 0 3.45 2 4 0 0 3.525 2 4 0 3.6 2 4 0 0 3.675 2 4 0 3.75 2 4 0 0 3.825 2 4 0 3.9 2 4 0 0 3.975 2 4 0 4.05 2 4 0 0 4.125 2 4 0 4.2 2 4 0 0 4.275 2 4 0 4.35 2 4 0 0 4.425 2 4 0 4.5 2 4 0 0 4.575 2 4 0 4.65 2 4 0 0 4.725 2 4 0 4.8 2 4 0 0 4.875 2 4 0 4.95 2 4 0 0 5.025 2 4 0 5.1 2 4 0 0 5.175 2 4 0 5.25 2 4 0 0 5.325 2 4 0 5.4 2 4 0 0 5.475 2 4 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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