No abstract

A robust and specialized time-integration scheme is proposed for the problem of the motion of a body under a resistive force,acting in the magnitude of the squared velocity of the body. Whereas standard time-integration schemes are well suitable with small time increments, they diverge with large time increments. The specialized time-integration scheme is keeping a good behavior with both small and large time increments.From the analysis of asymptotic behaviors, both near the initial state and far from the initial state, and by reducing the motion of motion into a scalar equation, we proposed an approximation of the solution, that keeps a good behavior both near the initial state and far from the initial state.Finally, we used the obtained approximation to implement a time-integration scheme, that won't diverge on large time increments.We compared the obtained time-integration schemes with other standard time-integration schemes.

A convenient approximated analytic solution is proposed for the problem of the motion of a body under a resistive force, acting in the magnitude of the squared velocity of the body. This solution is an explicit function of time, that keeps a good behavior both near the initial state and far from the initial state. To obtain a general analytic solution, we firstly used a reduction principle to be able to manipulate scalar objects, and we analyzed limit behaviors, both near the initial state and far from the initial state. Secondly, we proposed an approximated analytic solution with heuristics based on the built knowledge. Finally, a robust and stable integration scheme is proposed, based on the obtained analytic solution. We compared the scheme with other standard integration schemes.