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math245labprob01

# math245labprob01 - a = 2 and simulate the equation forward...

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Math245 Simulation Problem #1 Consider the 1st-order initial value problem (IVP) dy dt = σy + βy 3 , y (0) = y 0 , t 0 . In particular, consider two cases for the signs of the coeﬃcients σ and β . Case 1 : β = - 1 < 0; σ = a 2 > 0. dy dt = a 2 y - y 3 , y (0) = y 0 . Choose the value a = 2 and simulate the equation forward in time t 0 for the initial conditions y (0) = y 0 = 1 2 , ± 3 2 , ± 3 } . Plot all solution curves in the same ﬁgure. Case 2 : β = +1 > 0; σ = - a 2 < 0. dy dt = - a 2 y + y 3 , y (0) = y 0 . Choose the value
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Unformatted text preview: a = 2 and simulate the equation forward in time t ≥ 0 for the initial conditions y (0) = y = {± 1 2 , ± 3 2 , ± 5 2 } . Plot all solution curves in the same ﬁgure. Related material: Lab set #3 and #4 handouts. Work to be submitted: results(printed graphs) and print out of just one case of main program and ODE function ﬁle....
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