Question

Background The van der Pol equation is a 2nd-order ODE that describes self-sustaining oscillations in which energy is withdrawn from large oscillations and fed into the small oscillations. This equation typically models electronic circuits containing vacuum tubes. The van der Pol equation is: dy2 dy where y represents the position coordinate, t is time, and u is a damping coefficient The 2nd-order ODE can be solved as a set of 1st-order ODEs, as shown below. Here, z is a 'dummy' variable. dy dt dz dt The two 1st-order ODEs above are coupled and must be solved simultaneously. i.e. the solutions are dependent on each other and therefore cannot be solved individually. The first iteration will solve for y1 and z1 using initial conditions yo and zo. The second iteration will solve for y2 and z2 using y1 and zi, and so forth You are strongly encouraged to complete a few iterations by hand to fully understand the process.

Answer 1

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