These methods with or without the Jacobian are analyzed in terms of convergence and stability. In particular, it is proved that the proposed methods have a convergence order up to 4 regardless of the ...

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 ...

Now that I have an analytical solution, I can compare different numerical methods to this. Euler Method Let me go ahead and calculate the motion of this mass on a spring with the normal plain method.