Design and construct a computer program in one of the approved languages (C, C++, Java, Pascal, etc.) that will illustrate the use of a third-order explicit Runge-Kutta method of your own design. In other words, you will first have to solve the Runge-Kutta equations of condition for a third-order method. Be sure to follow the documentation and programming style policies of the Computer Science Department.
The initial value problem to be solved is the following:
x'(t) = (5 / (4 (1+t2))) x + cos(3 x)
subject to the initial condition: x(0) = 1.0
Obtain a numerical solution to this problem over the range from t=0.0 to t=3.0
for seven different values of the stepsize,
h=1.0, 0.5 , 0.25 , 0.125 , 0.0625 , 0.03125 , and 0.015625 .
In other words, make seven runs with 3, 6, 12, 24, 48, 96, and 192 steps, respectively. For each run, print out the value of h and then a table of t and x. The true solution of this differential equation resembles the following plot of x(t) as a function of t.
