Backward error analysis for conjugate symplectic methods

<abstract><p>The numerical solution of an ordinary differential equation can be interpreted as the exact a nearby modified equation. Investigating behaviour solutions by analysing is known backward error analysis. If original and share structural properties, then approximate geometric features such existence conserved quantities. Conjugate symplectic methods preserve form Hamiltonian when applied to system. We show how blended version variational techniques used compute structures. In contrast other approaches, our analysis method does not rely on ansatz but computes structures systematically, provided that formulation known. The technique illustrated example symmetric linear multistep with matrix coefficients.</p></abstract>