Find y(0.1) for `y''=-4z-4y`, `x_0=0, y_0=0, z_0=1`, with step length 0.1 using Euler method (2nd order derivative)
Solution:
Given `y^('')=-4z-4y, y(0)=0, y'(0)=1, h=0.1, y(0.1)=?`
put `(dy)/(dx)=z` and differentiate w.r.t. x, we obtain `(d^2y)/(dx^2)=(dz)/(dx)`
We have system of equations
`(dy)/(dx)=z=f(x,y,z)`
`(dz)/(dx)=-4z-4y=g(x,y,z)`
Euler method for second order differential equation
`y_1=y_0+hf(x_0,y_0,z_0)=0+(0.1)*f(0,0,1)=0+(0.1)*(1)=0+(0.1)=0.1`
`:.y(0.1)=0.1`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
