Write down the abstract formulas you are plugging in and only then plug in the s

Question

Write down the abstract formulas you are plugging in and only then plug in the specific numbers for the given. Appropriately tabulate all results.

A ball at 1200K is allowed to cool down in air at an ambient temperature of 300K. Assuming heat is lost only due to radiation, the differential equation for the temperature of the ball is given by

d(theta)/dt=-2.2067x10^-12(theta^4-81x10^8), theta(0)=1200K

Find the temperature at t=480 seconds using the Runge-Kutta 4th order method below. Use a step-size of h=240 seconds.

Rk4th:

k1=f(xi,yi)

k2=f(xi+h/2, yi+0.5 k1h)

k3=f(xi+h/2, yi+0.5 k1h)

k4=F(xi+h, yi+k3h)

yi+1=yi+h/6(k1+2k2+2k3+k4)

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