chapter5.page14

chapter5.page14 - Figure 9. Runge-Kuttas method for...

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14 1. NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS Solution Suppose y ( t ) = x 0 ( t ) is the velocity, then Rayleigh equation becomes x 0 = y y 0 = 2 y - 3 y 3 - 2 x So we apply the numerical method for F = y 2 y - 3 y 3 - 2 x and x 0 ( t ) = F ( t, x ) with x (t) = x(t) y ( t ) , x (0) = 1 - 2 . The following screen shot gives approximate solution using Runge-Kutta method,
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Unformatted text preview: Figure 9. Runge-Kuttas method for Rayleighs equation a we also plot the solution in xy-plane, which is called the velocity-position phase plane, with y-axis represent the velocity and x-axis is the...
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