Assume we throw a body from a height h with the velocity v0 in some arbitrary direction. Beside the weight W = mg, another force F(v) is acting (suppose this can be any weird function). We want to solve this problem without integrals - numerically.
So we assume that in a very short time dt the force F is constant and calculate the motion of the body as if it consisted of a lot of phases lasting dt, with a constant force. We write a program for this.
How can we then estimate the accuracy of our results (the maximal error) if we calculate, for example, the time T after the body will fall to ground, the velocity or the coordinates at some arbitrary time t_x? Of course we know the step dt.