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1. Consider the second order differential equation: where Y\" is the second deri

ID: 2886481 • Letter: 1

Question

1. Consider the second order differential equation: where Y" is the second derivative and Y' the first derivative of Y with respect to time. a. Convert this second order equation into a pair of first-order equations by first assigning a new name to Y'. b. At t = 0, Y = 1.0 and Y,-1.0. Using a full step-size of ?-0.1 determine Y and Y, at t 0.1 secs and t = 0.2 secs, using the 4th order Runge-Kutta method. c. Evaluate the Collatz criterion at the end of the second full step and comment on the step size.

Explanation / Answer

let Y'=p; so, y''=p'.

given equation is,

y''+(y')2/y=0

p'y+p2=0............will be the 1st order equation of 'p'.

where y'=p