Applying Euler’s Method and Runge-Kutta Method for Calculating the Motion of a Projectile

Question

Consider the motion of a projectile in 2D under a constant gravitational force, neglecting air resistance. Recall from Euler’s method for solving

dy/dx = f (x, y) is summarized by y_n+1 = y_n + ∆ xf (x_n, y_n); x_n+1 = x_n + ∆x,

in which we are determining the x and y values at the (n + 1)^th step from their values at the nth step, i.e. Euler’s method allows us to propagate the ODE to find values of y at a different value of the independent variable, x.

For the whole question please refer to the PDF document attached along with the solution.

Summary

The question belongs to Computer Science, particularly to C language. The question is about calculating the movement of an object in air under gravitational force with no air resistance with the help of Euler’s Method, Runge-Kutta Method. 3 programs with this regard has been written in C language. Please find the programs in the solution Zip file.

Total Word Count 226