Here is a plot of three things. First, the analytic solution, second the Euler method (as described above) and third the Euler method calculating position, then velocity, then acceleration.

This paper presents a class of numerical methods for the approximate solution of ordinary differential equations where the derivatives depend on the history of the solution. These methods, which are ...

The paper presents a new approach to the numerical solution of the Euler-Lagrange equations based upon the reduction of the problem to a second-order ordinary differential equation (ODE) on the ...

Numerical methods for differential and integral equations are indispensable in modern applied mathematics and engineering, offering tools to approximate complex physical phenomena where analytical ...