Question

Solve the set of differential equations using:
1) Euler's method.
2)4th order Runge Kutta method
assuming at t=0, y1=4, y2=6
integrate to t=2 with step size of 0.5
dy1/dt=-0.5y1
dy2/dt=4-0.3y1-0.1y2

Answer 1

@mathmate

Answer 2

not a question

Answer 3

@nastech
When are you posting the set of DE?

Answer 4

sorry I've edited the question

Answer 5

\[X=(x,y)=\left[\begin{matrix}0-0.5x+0y\\4-0.3x-0.1y\end{matrix}\right]\]

\[X(0)=\left[\begin{matrix}4\\6\end{matrix}\right]\]
Euler method step1 with \(\triangle t=0.5\)
\[X(0.5) =\left[\begin{matrix}4\\6\end{matrix}\right]+ 0.5*\left[\begin{matrix}0-0.5*4-0*6\\4-0.3*4-0.1*6\end{matrix}\right]=\left[\begin{matrix}3\\7.1\end{matrix}\right]\]

Answer 6

Euler method step2 starts from step1 is
\[X(0.5) =\left[\begin{matrix}3\\7.1\end{matrix}\right]+ 0.5*\left[\begin{matrix}0-0.5*3-0*7.1\\4-0.3*3-0.1*7.1\end{matrix}\right]=\left[\begin{matrix}2.25\\8.295\end{matrix}\right]\]

Answer 7

You do \(X(1.5),X(2)\)

Answer 8

Oh, I do it by hand, not sure what you want me to do. Matlab??