## Conservative numerical methods for $$\ddot x=f(x)$$.(English)Zbl 0561.65056

Two numerical methods are developed for solving the initial value problem $$\ddot x=f(x)$$, $$x(0)=\alpha$$, $$\dot x(0)=\beta$$. Both methods conserve the same total energy (kinetic plus potential) as does this differential equation, i.e. $${1/2}\dot x(t)^ 2 + \phi(x(t))$$. Here $$\phi(x)$$ is any function such that $$-d\phi /dx=f(x)$$. Two examples describe the situation.
Reviewer: M.Bartušek

### MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems
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### References:

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