# Can the numerical method for a set of ordinary differential equations be non-conservative?

I have a set of highly coupled ODE that I am solving. I'm just not understanding whether the quantities will be inherently conserved because it's an ODE. Everything I'm seeing on Google is for PDE's.

• One such problem is integrating an orbit in a gravitational field. We know that the energy and angular momentum are conserved in such problems. If there are errors in the numerical integration, these constants may not be conserved. I have heard there are integration techniques that deal with this, but am not familiar with them. Dec 1, 2016 at 21:16
• @RossMillikan : For conservative systems you can use symplectic integrators. They preserve the conserved quantities to at least the integration order, i.e., the drift away from a tightly oscillating near constant is slower than the order of the method. -- The most known and abused (in reducing it to symplectic Euler, not computing the force correctly,…) symplectic integrator is the Newton-Cromer-Störmer-Verlet method. See Hairer et al. on geometric numerical integration Dec 2, 2016 at 2:23