# odesys14ch6 - Numerical Solution of System dx/dt = f(t,x,y...

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b11b888f9635afa7d7fa55c0d41c8dcd29a3aa74.xls Page 1 Numerical Solution of System dx/dt = f(t,x,y), Name 20 40 60 80 100 120 140 160 Phase Portrait y
b11b888f9635afa7d7fa55c0d41c8dcd29a3aa74.xls Page 2 dy/dt = g(t,x,y) f(t,x,y) 0.25*x*(1-(x/200)-(y/50)) g(t,x,y) 0.10*y*(1-(y/100)-(x/100)) Initial Conditions Initial time 0 Final time 100 Initial x value 100 Initial y value 25 Approximation Data
b11b888f9635afa7d7fa55c0d41c8dcd29a3aa74.xls Page 3 0 20 40 60 80 100 120 Solution Curves x, y 10 15 20 25 30 y 0 50 100 150 200 0 x
b11b888f9635afa7d7fa55c0d41c8dcd29a3aa74.xls Page 4 # of subintervals 150 Phase Plane 250
b11b888f9635afa7d7fa55c0d41c8dcd29a3aa74.xls Page 5 t = Type Comments Here: 0 10 20 30 40 50 60 70 80 90 100 0 x(approx) y (approx) t 8 0 5 Scroll Me
b11b888f9635afa7d7fa55c0d41c8dcd29a3aa74.xls Page 6 0.00 80 100 120 140 160 180 200 x
b11b888f9635afa7d7fa55c0d41c8dcd29a3aa74.xls Page 7
b11b888f9635afa7d7fa55c0d41c8dcd29a3aa74.xls Page 8
Calculation Page 9 Calculation Sheet 0 100 25 0 0 0.3333 100 25 0 0.6667 100 25 0 0 1 100 25 0 1.3333 100 25 0 0 1.6667 100 25 0 2 100 25 0 0 2.3333 100 25 0 2.6667 100 25 0 0 3 100 25 0 3.3333 100 25 0 0 3.6667 100 25 0 4 100 25 0 0 4.3333 100 25 0 4.6667 100 25 0 0 5 100 25 0 5.3333 100 25 0 0 5.6667 100 25 0 6 100 25 0 0 6.3333 100 25 0 6.6667 100 25 0 0 7 100 25 0 7.3333 100 25 0 0 7.6667 100 25 0 8 100 25 0 0 8.3333 100 25 0 8.6667 100 25 0 0 9 100 25 0 9.3333 100 25 0 0 9.6667 100 25 0 10 100 25 0 0 10.333 100 25 0 10.667 100 25 0 0 11 100 25 0 11.333 100 25 0 0 11.667