From the Euler method to the closed-form solution of the motion of a particle influenced by linear velocity-dependent friction and arbitrary time-dependent driving force

Abstract

The Euler method of numeric approximation for solving initial-value problems is applied for describing the motion of a particle influenced by linear velocity-dependent friction and arbitrary time-dependent driving force. By employing the formula for the sums of powers of integers, it is shown that the recurrence relation obtained from the Euler method converges to the exact closed-form solution.

Keywords

• Euler method
• numeric approximation
• first-order differential equation