Using the Runge-Kutta 2nd order
Ralston method with a step size of 5 seconds, the distance in meters traveled by
the body from t=2 to
t=12 seconds
is estimated most nearly is
3904.9
3939.7
6556.3
39397
Q5. The Runge-Kutta 2nd order method
can be derived by using the first three terms of the Taylor series of
writing the value of yi+1 (that
is the value of y at
xi+1 )
in terms of yi (that
is the value of y at
xi)
and all the derivatives of y at
xi .
If h=xi+1-xi,
the explicit expression for yi+1 if
the first three terms of the Taylor series are chosen for solving the
ordinary differential equation
![](runge_2nd_method_files/image021.gif)
would be
![](runge_2nd_method_files/image023.gif)
![](runge_2nd_method_files/image025.gif)
![](runge_2nd_method_files/image027.gif)
![](runge_2nd_method_files/image029.gif)
Q6. A spherical ball is taken out of a furnace
at 1200K and is allowed to cool in air. Given the following,
radius of ball = 2 cm
specific heat of ball = 420
J/(kg-K)
density of ball = 7800
convection coefficient = 350
J/s-m^2-K
The ordinary differential equation is
given for the temperature,
of the ball
![](runge_2nd_method_files/image033.gif)
if only radiation is accounted for. The
ordinary differential equation if convection is accounted for in
addition to radiation is
![](runge_2nd_method_files/image035.gif)
![](runge_2nd_method_files/image037.gif)
![](runge_2nd_method_files/image039.gif)
![](runge_2nd_method_files/image041.gif)
Complete Solution
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