TY - JOUR
AB - The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward error analysis. If the original and modified equation share structural properties, then the exact and approximate solution share geometric features such as the existence of conserved quantities. Conjugate symplectic methods preserve a modified symplectic form and a modified Hamiltonian when applied to a Hamiltonian system. We show how a blended version of variational and symplectic techniques can be used to compute modified symplectic and Hamiltonian structures. In contrast to other approaches, our backward error analysis method does not rely on an ansatz but computes the structures systematically, provided that a variational formulation of the method is known. The technique is illustrated on the example of symmetric linear multistep methods with matrix coefficients.
AU - McLachlan, Robert
AU - Offen, Christian
ID - 29236
IS - 1
JF - Journal of Geometric Mechanics
KW - variational integrators
KW - backward error analysis
KW - Euler--Lagrange equations
KW - multistep methods
KW - conjugate symplectic methods
TI - Backward error analysis for conjugate symplectic methods
VL - 15
ER -