Numerical Methods Initial value problems (Second order differential equations).

Question

Numerical Methods Initial value problems (Second order differential equations). Consider the problem d2y / dx2 + dy / dx + y2 = x, y(0)=1, dy / dx(0) = 0 to compute a meaningful value for y(0.2). Transform the second order differential equation into a system of first order differential equations and then solve by first using a single step (h=0.2) and a repeat calculation using two steps ( h= 0.1 ). Compare the calculated values ofy and specify the meaningful significant figures in each calculation. Use the first order Euler's method to compute y(0.2): Use the second order Runge-Kuttta method to compute y(0.2): Use the second order Runge-Kuttta method to compute y(0.2):

Explanation / Answer

I would have loved to help you with this question but there are far too many to be answered in 1 post. Moreover it is also not in agreement with Cramster's rules! Hence please post a maximum of 2 or 3 questions in one post and i would try my best to help you. Hope you understand. Thank you!

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