# Thread: Nonlinear method for boundary value problems of a constant function.

1. ## Nonlinear method for boundary value problems of a constant function.

the question Im having a hard time dealing with is this equation
y"(t)=-g where g is the gravity at 9.8m/s^2
and the boundaries are
y(0)=0.9144 and y(3)=0

how to solve this problem? I am having trouble with runge kutta since it is only a constant function? what to do pls?
I need to know how many shots to and the graph. thanks

2. ## Re: Nonlinear method for boundary value problems of a constant function.

Hello, Marcorupert!

From your title, you're making the problem sound trickier than it is.

$\displaystyle y"(t)\,=\,\text{-}g\;\text{ where }g\text{ is the accel'n due to gravity at }9.8\text{m/s}^2$

$\displaystyle \text{and the initial conditions are: }\,y(0)\,=\,0.9144\,\text{ and }\,y(3)\,=\,0 .$

$\displaystyle \text{Find }y(t).$

We have: .$\displaystyle y''(t) \:=\:\text{-}9.8$

Integrate: .$\displaystyle y'(t) \:=\:\text{-}9.8t + C_1$

Integrate: .$\displaystyle y(t) \:=\:\text{-}4.9t^2 + C_1t + C_2$

We are told that $\displaystyle y(0) = 0.9144\!:$
. . $\displaystyle \text{-}4.9(0^2) + C_1(0) + C_2 \:=\:0.9144 \quad\Rightarrow\quad C_2 \,=\,0.9144$

We are told that $\displaystyle y(3) = 0\!:$
. . $\displaystyle \text{-}4.9(3^2) + C_1(3) + 0.9144 \:=\:0 \quad\Rightarrow\quad C_1 \,=\,14.3952$

Therefore: .$\displaystyle y(t) \;=\;\text{-}4.9t^2 + 14.3952t + 0.9144$

3. ## Re: Nonlinear method for boundary value problems of a constant function.

Thanks But I need to know the first shot of the graph in nonlinear method. :/