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

Greenspan, Donald

J. Comput. Phys. 56, 28-41 (1984).

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

Keywords:

computer examples; energy conserving methods; conservation laws

References:

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