Please answer the following questions in complete sentences in a typed manuscript and submit the solution on blackboard by on April 25th at noon. Submissions will be accepted and graded at any point before the final exam is given, however, any submissions turned in after April 25th cannot be guaranteed to be graded before the final exam.
Please identify anyone, whether or not they are in the class, with whom you discussed your homework. This problem is worth 1 point, but on a multiplicative scale.
Make sure you have included your source-code and prepared your solution according to the most recent Piazza note on homework submissions.
Consider the ODE with .
Apply the stretching transformation to obtain the equivalent ODE And show the relationship between and .
Show that applying the forward Euler method to the ODE for in with step size is equivalent to applying the same method to the ODE for in with step size that satisfies .
Consider the following system that describes the behavior of two masses in the presence of a third mass of (small) size. The masses are and (earth and sun): The initial conditions are Let .
Implement a 4th order RK method for this problem.
Show what happens for , and , , steps. Discuss any interesting observations.
(Not required) Use a standard integration software package
such as ode45
or an equivalent to look at the result.
Newton's equations for the motion of a particle on a planar orbit (with eccentricity , ) are