I'm new to numerical analysis and got stuck on an ODE: y′′+y^3−0.5=0 with h=0.1, y(0)=1 and y′(0)=1. How should I begin?

Bellenik3

Bellenik3

Open question

2022-08-20

I'm new to numerical analysis and got stuck on an ODE:
y + y 3 0.5 = 0
with h = 0.1, y ( 0 ) = 1 and y ( 0 ) = 1.
How should I begin?

Answer & Explanation

Terry Avery

Terry Avery

Beginner2022-08-21Added 10 answers

Start by defining a new variable satsfiying z = y . Then rewrite your second order equation as a system of first order ODEs:
{ z = y 3 + 0.5 y = z
You can then solve these two equations simultaneously with the Euler method.
alexmjn

alexmjn

Beginner2022-08-22Added 4 answers

Ah right, of course.

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